hello everyone welcome to our lecture in general physics 1. in this video we're going to discuss introductory topics in physics highlighting the basic concepts in measurements our objectives is to solve measurement problems involving conversion of units as well as to familiarize the different fundamental units and um the different systems of measure and to express measurements with correct significant figures and in scientific notation so let's start with measurement so but first again so the flow of discussion is discussion of the concepts and for our um for our class participation for the concept builders you may submit your answers in the public link provided so you may pause the video once we get into the concept builders you may pause the video and just resume watching after you submitted your answers so let's start with measurements so so when we want to quantify or when we want to numerically describe um the property of an event a property of an object or characteristics of an object we can do it in two ways so first we can do it by counting so sabinatin dibasia statistics there are those data that can be counted or the countable data so if you think that the data you needed is countable then proceed with the counting method however we know that most of the data needed especially in physics because physics is an experimental science so the data needed cannot be um counted so we cannot use counting methods in those cases we use instruments to provide the numbers we need them so in those cases where we use instruments to gather or to get the numerical value needed we need to perform measuring the process of measuring so measurement is the process of assignment of numerical value to an object's physical properties so in physical properties just take note that physical properties is synonymous two dimension and we'll learn this later so synonymous dimension when we use numbers to describe a physical property we must always specify the unit that we are using so we need to assign units to the numerical quantity of measurements to convey the relative size or the relative magnitude of the property we are describing so we need to assign units to the numerical quantity so when we incorporate the magnitude or the numerical quantity so if we incorporate this with the corresponding units this is now called a physical quantity so the backup quantity in civilian is referring to a number so quantity physical quantity so physical quantity is any number that describes a physical property so that is what is a physical quantity quantities whole nand submodule not a new definition and i think physical quantity so again capacity nothing physical quantity it must be a number together with the corresponding units so for example 9 meters so 9 is the number meter is the units or 20 kilograms so 20 is the number kilogram is the unit so that is a physical quantity so servitude is important because um by by assigning units uh to the numerical quantity we are able to convey the relative sizes of the property or the relative magnitude of the property so for example sales person bibliography so if you just um if you just mentioned nine there is no meaning to these numbers a number is just a number unless you place a meaning to it i don't know meaning this beat us a number nine that is the unit of measurement so instead of instead of um saying nine just say nine inches or um then just include whatever unit they are using however in real life situation since it is customary size 9 or size 6 size 10 refers to inches so he didn't attend in real life but technically you need to include so malay mode wrong size 9 centimeters so you need to um you need to to [Music] incorporate the corresponding units to the magnitude in order to describe a physical property in physics or or generally in science there are seven fundamental quantities that um numerically represent the seven primary dimensions or the seven fundamental properties of an object so to define fundamental quantities as an ion and so fundamental quantities are basic quantities that are independent from one another so the units that corresponds to the fundamental quantities are called the fundamental units or the base units so here are the seven fundamental quantities so we have here the length the mass the time temperature electric current luminous intensity and amount of substance but if you want to easily recall this you can um you can just recall this one so m e t t a l l so m for the mass e for electric current t for time another t for for temperature a for amount of substance l is for the length and l is for the luminous intensity this is an easy way to recall the seven fundamental quantity so metal but with double t and double l so since there are seven fundamental quantities there are also seven fundamental units that uh measures these quantities so ito young seven fundamental units and these are the symbol of these units so um fundamental units are since these are fundamentals have been attained so these units are also called base units and base units furtherly divide into or well um you cannot derive these units from other units so xiaom basic units to build other units or to build other quantities so before we discuss the right quantity so to differentiate um base quantities or fundamental quantities or the base units from the derived units or the derived quantities base units are those so base units are those which can be defined as an intention which can be defined only by the way it was measured we cannot derive the the base units as a base units so we cannot derive it from from other quantities so the the basis for this base units to be defined is only by the way it was measured so let's go to your module and um look at some of the examples so here are the the the quantity fundamental quantity with the corresponding unit so this this um the unit the base units of this corresponding quantity is only can only be defined by the way it was measured for example one meter is the distance traveled by the light in a medium during a time interval of one over 299 million seven hundred ninety two thousand four hundred fifty eight fraction of a second so another example would be one kilogram is the standard platinum iridium cylinder kept at the international bureau of weights and measures in front so if you if you read this description or definition of one kilogram what is a one kilogram edible maintenance so this is the way on how they obtained um one kilograms in real life so that's how they define these fundamental units and the same with the other fundamental units so that's how they define it so compared to the derived units so derived units and derived quantities are resulting from the combination of any of the fundamental quantities or when we say derived units derived units those are quantities or units defined by describing how it was calculated from other quantities so may it be a fundamental or another derived quantity so to give you an example these are the common derived quantity so we have your speed meters per second acceleration area volume force and energy so for example let's take force so if we define force force is the product i sorry so must have production so product of mass and acceleration so this is a fundamental quantity and this is a derived quantity so this is a calculation about how to solve for the force definition so force is defined as the product of mass and acceleration and for example speed is um distance divided by the time elapsed or acceleration is equal to market numbers okay so acceleration is equal to um the change in velocity divided by the time interval or the time elapse so as you can see these derived quantities are defined by the way it was calculated other quantities to get the value perov fundamental quantities it was defined based on how it was measured so companies are miniature in real life union definition fundamental quantities and fundamental units nothing okay so let's have a concept builder so bhagavataya move on systems of measure let's have a concept builder so identify whether the si unit needed to describe the following scenarios are base units or derived units so you can answer this in the padded link provided so you may pause this video and then resume watching after you submitted your answers okay so let's answer number one so number one sabudito the speed of gliding down the zip line of embarcadero so here we need to identify whether the units needed are base units or derived units so we know that speed to to define speed it is the total distance divided by the total time so therefore since we define it by the way it was calculated next is power consumed by the province of albay so young power okay so young power so power is unneeded not in general units are derived because power is what's divided by the change in time so how about the height of my own volcano so height is a measure of length so therefore height so not in angle is a fundamental quantity therefore um height can be described using a base unit or fundamental unit or base unit so how about water pressure in ligaspecity so pressure can we describe it using a base unit or a derived unit okay so pressure can be described using a senayon okay using a derived unit because the pressure device force divided by the area for spare area last we have distance from sawangan park to bosails so distance is a measure of length distance is a measure of length therefore this can be described using a fundamental unit the two most widely used systems of measurements or the metric system and the english system in modern days metric system is also called as the s i units or the system international units or international system of units so there are two variations of metric system so first is the mks system and second is the cgs so mks stands for meter kilogram and second system while cgs is four centimeter grams and second system so depends upon a classic experiment i'm gonna go sometimes it's mks or sometimes cgs so while um english system is also known as the fps system or the foot pound satan system so it is also called as the british system or before it is known as the imperial system so most countries around the world so most of the regions around the world make use of the metric system as the basis for their standard unit of measurement so it must so while english system um there are only three countries left that make use of english system as their main system of measure so those countries are the usa myanmar and the liberia so these countries mainly use english system as their system of measurement but take note that from time to time we can use english system in philippines for example use a metric system but from time to time if it is needed we can use english system or we can use metric system so we can switch back but but the main uh main system of measure stand for standard measurement nagina gamma nang philippines and the rest of most of the the countries around the world is the metric system so here are the units corresponding units for the seven fundamental quantities so for length we have here the meter for mass kilogram for time second for temperature we have kelvin um electric current we have ampere luminous intensity candela and for the amount of substance we have mole and of course you need to familiarize yourself with the symbol and some of the other common quantities are the following and the corresponding units so just refer to your module for this table and a mancha so most of the countries or regions prefer metric system because it is easier to relate or convert smaller units to its equivalent larger unit of measurement for the same physical quantity so the value of the different fundamental and derived quantities is sometimes composed of very large or very small numbers so in in converting from from your base unit to its larger equivalent or a smaller equivalent of course you need some conversion factor so in matrix system it is easier because you just need to recall this exponential factor of multiples of 10 raised to a certain degree of exponent so for example a scenario so for example you want to convert one meter to kilometer so here if you can see so one meter is equal to one thousand kilometer iso one one kilometer is equal to one thousand meter so one thousand you can also use one kilometer is equal to 1 times 10 raised to 3 meter because 1 times 10 raised to 3 is equal to 1000 so for example you want to convert 1 meter to parameter stereometer again so just recall that that one parameter is equal to 1 times 10 raised to 12 meters 1 times 10 raised to 12 meters so instead of writing this very long sequence of number just use this exponential factor yeah so kappa positive so if this is our base unit top positive one exponent nothing base positive exponent numbers ebig sabine larger young unit compared to the bc unit negative exponent nothing big um smaller young unit unit so this is for um this is for converting from the base unit to smaller and larger units of length so meter so padding governs unit converted units so in metric system it is easier to convert because the conversion factor is a multiple of 10 raised to a certain degree of power so unlike in the english system which has no pattern or has irregular values as um conversion factors for example for example in the english system so if you want to convert um if you want to convert inches one inch to feet or one and a papa one yard to feet so feet and then one mile to its equivalent feet so as you can see so inch inches is inch is smaller than the feet yard is smaller than feet minus is smaller than feet so if you look at the equivalence for example in one feet there is 12 inches or in one inches one inch in one inch rather there is one over 12 feet so in one yard there is about three feet and in one mile there is 5280 so if i'm not mistaken fit so as you can see um there is no pattern so there are irregular patterns to the equivalence between um between smaller and larger units of the same physical quantity so in this case this is a measure of length so there is no pattern in in the conversion factor and the equivalence of smaller and larger physical quantity units of the same physical quantities for english systems so unlike here that you just need to recall that you need to multiply it by 10 raised to a certain degree so multiples of 10 amp converts a symmetric system so this is also the the main reason why most of the countries change from using english system to metric systems gold nut then is to secure accuracy and reproducibility or precision in the result of our measurement in our experiments accurating measurement and as well as precise or reproducible reproducible experiment to do that to to determine or to monitor the reproducibility the precision of the result the same unit of measurement experimenter so how do we now convert from one unit to another unit so what units describe are the different dimensions of the measured objects so therefore to convert from one unit to another unit we need to perform dimensional analysis so dimensional analysis is a process of using units so this is a process of using units or dimensions in solving problems so basic application of dimensional analysis is you need conversion so where we equate value of a certain unit to its equivalent units of the same physical quantity so for example we have here 9 meters so we equate it to its equivalent value in another unit of the same physical quantity so for example you would like to know its equivalent value to um using centimeter as a unit so i know young new value and how do we find this value so to convert we need to identify the conversion factors which can be used to eliminate and change units to your desired units the conversion factors are numerical fraction and so these are numerical fraction or ratio between quantities which can be used as a multiplication factor for converting one units to another so the following are the common conversion factors as you can see these are the equivalence between one unit two to another unit of the same physical quantities for example here this is for the different units that measures or describes length dimension of length so here for the dimension of mass dimension of time speed force and other quantities so derived may be derived and fundamental quantities so you can also use the table of prefixes so you can also use this table of prefixes in your um as your basis for conversion factor so just recall or just take note of the prefix to be used and so that the prefix the corresponding prefix that describes this exponential factor and of course this unit equivalent so for example in order to convert one meter to parameter or to convert meter to parameter the conversion or the equivalent is that the unit equivalent is that um so the the unit equivalent is that one parameter is equal to one billion one trillion one trillion meters or to avoid this long sequence of number it is equal to one times ten raised to meters positive 12 times 10 raised to positive 12 you know that the equivalent unit is one tera meter or parameter so you will know that it is four nanometer so let us have some examples so by the way here are the steps in unit conversion so first you need to identify the value to be converted so sometimes it is already given explicitly given you values to be converted but other times it is in problem solving but sometimes problems now convert 70 meters per second two kilometers per second so identify anybody you need also to identify yeah and then step two is to find the conversion factor so the equivalence unit equivalence and the conversion factors that can be used to change the unit so just refer to the table of graphics and the table of the conversion factors for your for the unit equivalents and conversion factors so step three is to multiply the original value to the conversion factor to eliminate and change the unit so it is important also to know how to set up your conversion factors so it is important to know how to set up your conversion factor so which for example we have here one meter is equal to um 100 centimeters a numerator denominator before we multiply our original value to the conversion factor yes individual conversion factor is a ratio so alindito into fraction and last step is of course to write the equivalence of course one word problem you need to write it in a whole sentence on how to describe that value so let's have some example okay so suppose you would like to convert yeah 396 meters to its equivalent value in kilometers so how do we now find this value so first so of course we need to look for the conversion factor so so the the unit equivalent so since we want to convert meter to kilometers unknown conversion factor between meter and kilometer so we know that one kilometer is it is equal to 1000 meters so step one in converting is to write down the original value together with its units and then multiply it by the conversion factors so if we write this as a fraction so we know that this is 300 the same as 396 meters divided by one so since as we can see in this um expression meter is at the denominator at the numerator so to eliminate this meter one thousand meter sila sedina minitor so we'll write one thousand meter in the denominator and then kilometers a numerator so now we can cancel meters in our equation in our solution so then perform the ratios 396 times one divided by one thousand so we'll have zero point kilometers so 396 meter is equal to 0.396 another example example number two suppose you would like to convert 60 miles to fit 60 miles repeat so one one mile is equal to 5280 feet step one so write down our um original value 60 miles and then times so we would like to eliminate miles therefore we will write one mile don't store and then write this value so this is our conversion factor now so we cannot eliminate miles from our solution and perform the operation to get the new value so 60 times 5280 that would give us 316 thousand eight hundred feet so now we know that sixty miles is equal to three hundred sixteen thousand eight hundred feet so you can also write this if you would like to express this in the correct number of significant figures you need to count the significant figures in your original value so here we only have one significant figure so therefore if we write this express this in correct significant figures we'll have 16 miles is equal to so here three so since the customer d3 is one we don't need to change this number so just retain three and then zero zero zero zero zero okay so in correction with correct using significant significant figures it'll 800 feet so as you can see it is easier to convert in metric system because the conversion factors are in multiples of 10 so raised to a certain degree so unlike in the english system where it has no pattern or has irregular values as conversion factor so to compare so for example we would like to convert one meter to kilometer so we know that one that one kilometer is equal to one times ten raised to three meter or if you want to convert meters to nanometer so 1 nanometer is equal to 1 times 10 raised to negative 9 meter or to parameter for example one parameter so we know that one parameter is 1 times 10 raised to 12 meter so you just need to remember this um this exponents and their corresponding prefix s for 12 positive 12 we know that it is quarter negative negative 9 is nano so 3 positive 3 is kilo so just refer to the table of graph excess for the prefixes exponential factor and unit equivalence so you can you can also apply those not just in meter but in other metric units yeah so for example but in kilogram or other quantities other physical quantities unlike in the english system so for example the biome feed so for example inches to feet so one inch is equal to 1 over 12 fraction of the feet so for example another one yard is equal to about three feet so one mile is equal to 5280 feet so as you can see there are no patterns in order to easily recall the equivalent or the conversion factor for the english system so that is why most of the countries have been attending that most of the countries prefer using the metric system of our system for standard measures unit of measure so we can also convert values from metric units to english units and vice versa so for example yeah equivalence to be used as conversion factors so between unity between metric units and english um units for example little one inch is equal to two point fifty four centimeters so inches deba is for english part of english system it is metric system so feet two meters miles to feet two kilometers miles to feet five meters to feet yeah so we have here other also so young time the same launcher for for english and for metric system so just refer to your so let us have again another example let's have another example so suppose we would like to convert example number three convert 47 centimeters to its equivalent value in in chest so this is from metric and then convert attention to english units so how many centimeters are there in inches so if we look at our table so there are 2.54 centimeter in one inch in one inch there are 2.54 centimeters so using this equivalence we can create the conversion factors again for converting step one is to write down our um original value together with its unit and then multiply it by the conversion factor so the conversion factor since we would like to eliminate centimeter so we'll write 2.54 cm in the denominator and one inch in the numerator so we can now cancel out centimeters and then perform the operation so 47 times 1 divided by 2.54 will give us 18.5 inches so since there are two significant figures in our original value so to correctly express this one so 47 centimeters all right let me check on your exact value 47 developer decimal so if we if we would like to express this one into correct number of significant figures since there are two significant figures in our given then 47 cm is equal to so since i'm concentrating is 5 we need to round up this number around this up so 19 inches 47 cm is equal to about 19 inches so there are also times where we do not have direct conversion factors between units and so we need to look at the units equivalence with other units for example yeah so let's have example for example we would like to convert 8.65 years to its equivalent number in seconds so we do not have the exact number the exact unit equivalence between years and seconds but we know that one year so one year is equal to 365 days we also know that one day is equal to 24 hours about 24 hours so we know that 24 hours i want r one r so one r is equal to 60 minutes and one minute is equal to 60 seconds so using this information we can now solve or we cannot convert years to second so first let's write down our original value which is six point eight point sixty five years and then since the original value nothing is not here so look look for the equivalent unit equivalent with years so here is one year is equal to 365 days here's a denominator eliminate and then 365 days at us so we can now eliminate this one and then so young performing operations conversion factor so next so convert this into ours so yeah so one day and then 24 60 minutes and now we need to eliminate we need so we have here one minute equal 60 seconds so since that's a numerator shot set in a minute or you minute so one minute excuse me is equal to 60 seconds so eliminate minutes so now you can now perform the operation so 8.5 8.65 times 365 times 24 times 60 times 60 this will give us the following results so 8.65 years is equal to 272 million seven hundred eighty six thousand and four hundred seconds so there are 272 million 786 thousand 400 seconds in 8.65 years so if you would like to convert or to express this incorrect number of significant figures so just count again how many significant figures are there in the event so we have here three significant figures so to write down your answer in correct significant figures so we can say that 8.65 years is equal to so we have here one two three so two hundred seventy so another question would be two so we have here seven so we need to run this up so 273 million seconds so that is the correct way of of writing it so writing it with correct number of significant figures 273 million so the technique here madame conversion factors is to write first the letters or the units before the number so determinase you need to be eliminated for example then to cancel it out you need to write the value the multiple the the the conversion factor in the conversion factor you need to write the same value or the same unit in the denominator and as a denominator you need to write it in the numerator in order to concentrate so this is a simple application of dimensional analysis where we are using units of the same dimension in simple conversion so let's have another example so what about we want to convert 12 um square meter to its equivalent value in square centimeter so we'll add entire unit given value inside and attend conversion factor but we know that one meter is equal to 100 centimeters so using this information we can now um convert 12 square meter to 12 square centimeter so write down our original value times the conversion factor so dito we would like to eliminate meters so again one meter 100 centimeters meter so therefore we need to write down again so one meter and then 100 centimeters nothing operations meter lito meter detail and then centimeter time centimeter will give us square centimeter so multiply the value in alpha 12 times 100 times 100 will give us 100 120 000 square centimeter so now 12 square meter is equal to 120 000 square centimeter so you can check for the number of correct sig figs so yeah so marathon the lowest so this is already in correct number of significant figures so there are also problems where um we need to convert only one part of the units for example somehow word problem diva sometimes in the derived units you only need to convert one um dimension of that of the specific physical quantities for example in speeds 55 kilometers per hour for example and then you would like to convert it into meter per second so for example we would like to convert 10 miles per hour two kilometers per hour so we don't need to convert but litto we need to convert miles to kilometers so there are problems where in the bythology only part of the of the whole unit so in this um type of situation so modeling them so i just identify again your conversion factor needed so how many kilometers are there in miles so let's look at our conversion factor so in one mile there are 1.609 kilometers so one mile there are 1.609 kilometers so we can now perform the unit conversion so 10 miles over per hour times the conversion factor so here since that's a numerator miles we need to write one mile in our in the denominator and then 1.609 kilometers in the numerator so we can now cancel miles and perform the operation so we have now here 10 times 1.609 is equal to 16.09 kilometers per hour so 10 miles per hour is equal to 16.09 kilometers per hour so yeah so if you would like to express this again into correct number of significant figures then you need to round this off into parama is some significant so 10 miles per hour is equal to yeah so since 6th so that is the equivalent incorrect number of significant figures pero you saw number of significant figures we have here 20 kilometers per hour so let's have another example example number seven so how about the long unit conversion i can say some value so again so 55 kilometers per hour and then we would like to express it into meters per second so young kilometers mr not any convert to meter and then you are we would like to convert the second so so we need to again identify the unit equivalence for each of the units to be converted so in one kilometer there are 1000 meters and in one hour yeah so one already 60 minutes and then in one minute there are 60 seconds you can also use um one rs equal to 3 600 seconds so if if you would like to use that but here i'm going to to demonstrate the longer method yeah longer conversion so step one write down our original value with its corresponding unit kilometer per hour times before the number so we can now cancel out one kilometer in our solution so now we can now write the conversion factor for ours so ours one r is equal to 60 minutes but what we want here is a second so therefore we need to convert minutes into seconds one minute and then so one minute is equal to 60 cents and we can now perform the operation so carpal tunnel form not in operation so we'll get that 55 kilometers per hour is equal to 15. meter per second or we've expressed to correct number of significant figures since the lavato so we need to round this up to two significant figures so 55 km per r is equal to 15 meter per second so here are other examples so this is a word problem so here in the fifth touchdown by sena against tokobari scoreboards here on 40r dash at a speed of 8 yards per second to express the speed in meter per second if one yard is equal to 0.9144 meters so in some of the problems given naom you need equivalence but in other problems you can just refer to the um conversion factor table so i'm giving up then we have here 40 yard and then we have your speed of 8 yards per second so we need to convert somebody to express the speed in meter per second which is 80 yards per second so you need to identify which of the values are needed to be converted so little eight yards per second and express it two meters per second so on conversion factor in attend one yard is equivalent to zero point nine one four four meters again a tensive meter sanju merit or nc yard sadena minitor parama eliminate nathaniel yard and then perform the operation so that you get this value so if if we need to express this in collapsing fig then 8 yards per second is equal to 7 meter per second so using correct significant figures so example another example suleiman sudan waterfalls in the elite cities the highest two-tiered waterfall in the philippines so with a combined drop of 470 meters so express this drop in feet so how many feet are there in meters we have 3.281 feet is equal to one meter so since i'm given a tennis meter so since given a tennis meter nothing eliminates meters without again attendance one meters and then a minute paramount eliminate and multiply it with our um with 3.281 feet so you'll get 885.86 feet so it will express them attention with correct significant figures 885.9 feet so we need to express it we correct number of significant figure so let us proceed to our concept builder express the following units in the desired unit of measure so number one express the speed limit of 65 miles per hour in terms of meters per second so we need to convert this unit into this unit and number two an athlete maintains his body mass index or bmi to normal so his mass measures 75 kilogram and has a height of 1.85 meters so if bmi is defined by the equation below find the body mass index of the athlete in pound pounds per square inches so did he maintain a normal body mass index so your normal body mass index nothing for millennia so bmi is equal to weight divided by squared height squared of height so sports uh science weight mini measuring in terms of kilograms so that's why you standard measure or unity bmi is kilograms per square meter so to answer this part just refer to this table so let's answer now number one so by the way um before you proceed to the next part of this video so answer part you may pause this video and just resume watching after submitting your answers to the given public link so number one so first we need to identify the value to be converted so here we need to convert 65 miles per hour into meters per second so we need to find the equivalent value in terms of this unit so we want to convert miles to meters and then hours two seconds so step two is to find the conversion factor so i'm in conversion factor not and we need to look into the unit equivalent so in one mile there are 169.34 meters and in one r there are 3 600 seconds but conversion factor is a ratio or a fraction so therefore to um find the conversion factor we need to base um we need to base it to the given value so para malama yogis in our given value 65 miles per hour so we want to eliminate miles so therefore we're going to write miles at the denominator of our conversion um conversion factors a ton conversion factor nothing and nothing conversion factor we need to to write so our palette so we need to write ours at the numerator of our conversion factor because in the original value that's a denominator so so capacitor we know that we can eliminate those units so solution 65 miles per hour times one thousand six hundred nine point thirty four meters divided by one mile sodium eliminated miles times the second conversion factor one r over three thousand six hundred seconds so d though we will be able to cancel out this one so r so material analysis meter per second so just perform the operation so we will get 29 meters per second so final answer nothing will be 65 miles per hour is equal to 29 miles per second so take note also of the significant figures number of significant figures original melancholium two significant figures then don'ts a converted value not end up but two significant figures then so for number two so we would like to find sold for the body mass of the athlete so bmi is uh measured or described by kilograms per square meters standard unit yeah and we would like to know the equivalent value of the bmi of of this athlete into its equivalent value in pounds per squared so again you formula for bmi is equal to weight divided by the height so science height squared weight is described by kilograms in kilograms but in real reality in physics it is mass in kilogram so yeah so so first step is to identify the given we have here the mass 75 kilograms and the height is 1.85 meters and identify the conversion factor so we have 2.205 pounds in one kilogram and since we want to convert squared meter into squared inch we don't have direct conversion factor between meters to inches so therefore we need to convert this into feet so you could convert an attention and then from feet we will convert it into inches problem you need to solve first for the problem before conversion for example of cbm i sold first for the bmi and then followed by the conversion of the value kopinapahanaxi force acceleration speed sold first for those of needed quantity before you do the conversion so for the solution so hanapin attends bmi using the formula so 75 kilogram divided by 1.85 meters squared so you making sure not engine class is 22 kilo kilograms per square meter so naka sulatna sakurak number of significant figures because in our given the least number of significant figures is tu so angeliba so just refer to the rules of multiplying numbers incorrect number of significant figures so now that we have the value for the bmi we cannot convert this into its equivalent value in pounds per squared inches so again in converting right first the original value so we have here 22 kilogram per square meter times so now i'll indeed we are going to write one kilogram at the denominator of our conversion factor and then new pounds we will write it in our numerator oh yeah and then multiply again you meter nothing this is meter times meter so we need to to cancel out um these two meters parama convert natanza cancel meters and then convert it into feet so therefore since the lower the one meters and then again one meter over three point two eight one feet so now we can um cancel out meters and another meter so and then what we want to do is to convert meter into inches or square meter into squared inches therefore from fit we need to convert it or multiply it to the conversion factor of feet and inches so there are um in one feet since nasa denominated there are 12 inches so inch times inch is squared inch so your final answer in another ion is that 22 kilogram per square meter is equal to two 0.03129 one four pounds per square inches however since don's original value not in meron and cayenne two significant figures we need to express this also into two significant figures so i'm gigging final answer not engine is that 22 kilograms per squared meter is equal to 0.031 pounds per square inch so in expressing values incorrect number of significant figures you need to recall how to round off numbers for example at long young hangang 31 long tayo so you need to um round this number off so so one more time two so since two but five just retain one so not id so my additional question detail which is uh did the athlete maintain a normal bmi so to answer this we need to refer to the table so again you ginagamit no bm my standard unit is kilogram per square meter so i'm gonna meet an attend to determine whether the bmi is normal is this one so balik tayo don't slide table nathan 224.9 evaluation is normal so therefore the athlete maintained his normal body mass index so we saw in our previous examples how units can be used to solve a problem or how units can be converted to other units so the process again the process of using units and dimensions in solving problem is called dimensional analysis for example sodito so since we know the dimensions of bmi or the unit of bmi we were able to define how the the the formula for bmi so um formula bmi but since i know that the the units that define or describe bmi is kilogram per squared meter some something some property that that can be described using kilogram and a property that can be described by meters and then it was a given problem nothing is equal to 75 kilogram and we have here also the height which is yeah it's 1.85 meters so therefore kilogram is a measure of mass and then meter is a measure of height it's a unit that describes height and then since square detail is to get the value of bmi so again yeah dimensional analysis the process of using units and dimensions in solving problems and to define dimension dimension is any physical property that can be observed or measured so since definition so in a sense dimension is synonymous or basically just the physical property so since there are seven fundamental properties or fundamental quantities there are also seven fundamental dimension or they called it seven primary dimensions and here are those seven primary dimensions so we have here the length the mass the time temperature electric current luminous intensity amount of substrate so refer tiles and dimensions fundamental dimensions and these seven fundament fundamental dimensions is used to describe different physical properties man i capital letter i luminous intensity capital letters and for amount of substance letter and capital letter n so some of the physical um common physical properties with its dimensions are the following so since madame problems of physics general physics common um physical properties we have the position the speed the time and the acceleration and here are the symbols of this one equation x v t and a and the units that describe these properties are so again for position we have meters so we know that meters is a measure of length so that's why and dimensional position is length so if dimensional money speeds the speed is defined as distance divided by time so therefore meron dion meter per second as the standard unit and meter is a measure of length and second is a measure of time so second again is a measure of time for time and for acceleration meter per second squared so we have here length divided by t squared time squared so it is important to learn dimensional analysis because it help us to solve for unknown dimensions of physical quantities or properties and check whether equations are dimensionally correct so for example hana plantain example for example so we define speed as distance divided by the time so the standard unit of of speed is meter per second so since so since this is the standard of unit of speed so therefore d must be something distance must be something that can be measured using um meter and time must be something that can be measured using second so however there are cases one meter per second speed nut and he no measured in terms of this one kilometers per hour for example describe it using kilometers per hour or sometimes miles per hour that this unit also describes speed so this unit also describe speed superno not in that we can also use this unit to describe speed so so in this cases instead of using unit to check whether something is dimensionally correct we can use the dimensions dimension is more so speeds have been attained and dimension speed so on meter is a measure of length second is a measure of time so january dimension is speed kilometer bus for example theta four kilometers so dimension speed is length divided by type so on standard unit is meter per second by sayana is a correct description you need for speed so in kilometer but is it a measure of length so the by kilometer is a measure of length so you are is also a measure of time so therefore kunti tignan kilometers per hour young dimensional is length also length divided by time and comparing it to the dimension of spin so therefore so this unit a pack my given count kilometer at my given kang arse it can be used to solve for the speed of your moving object so the same with miles per r so miles is a measure of length and r is a measure of type so therefore solution is a problem that our equation is dimensionally correct so another would be the equation of force equation of force so where force is defined as mass times acceleration force [Music] newton is just kilogram times meter per second squared properties is the same as the units no acting force so mass is mass is described using kilogram and then acceleration is described by meter per second squared so therefore if you get the product of these two units in terms of the dimensions included so kilogram is a measure of mass meter is a measure of length second is a measure of time and since this is squared so t squared so young measure of mass m measure of length divided by the measure of time squared so which is this one so take note class for example and then t squared over l you divide the time squared by the length instead of dividing the length by the time squared so hindi narinsha hindi narinsha tawagjan squared with so let us have a concept builder so again you may post this video and then just resume watching after you submitted your answers in the given patent link so state yes if the statement is correct and no if not so number one so is it possible for two quantities to have the same dimensions but different units so is it yes or no so number two is it possible for two quantities to have the same units but different dimensions number three you can always add two you can always add two numbers with the same units such as six centimeters plus three centimeters so can you always add two numbers that contains the same dimensions such as two numbers with length as dimensions so is it yes or no okay so to answer this question number one so is it possible for two quantities to have the same dimension but different units so okay quantities have the same dimensions but different units so for example putting measures in terms of meter per second and miles per are so they have the same dimension so you meter per second have uh length over time i am your miles per hour number 10 over time so therefore it is possible for two quantities to have the same dimensions but different units so number two is it possible for two quantities to have the same units but different dimensions so an answer deto is no s so number three so you can always add two numbers with the same unit such as six centimeters plus three centimeters so can you always add two numbers that contains the same dimensions such as two numbers with length as dimensions so is it yes or no so the correct answer here is example numbers with the same dimensions so the answer here is no okay so let's just have another concept builder so you may pause this video and then resume watching after you submitted your answers in the given pandemic so concept builder four right dimensionally correct if the units on both sides of the equal sign is consistent with each other and dimensionally incorrect if not for number one we have here x is equal to v times d sub n so let us see the dimensions the units of this equation so we have here x is equal to v times t so where this is the position this is for the speed or the velocity this is time so we know that the unit standard unit for position is meter for velocity or for the speed we have meter per second and for time we have second so if we perform this operation so these units will cancel out so not the meter is equal to meters describes dimension of length so another determinant of another meter second describes the dimension of time and we also have here another dimension of time so if we perform the operation algebraically so this will cancel out so the the dimension left are left in both sides so since para ocelon dimension of length so we can say that this this equation is dimensionally correct so if it's a b we can use this equation we can use this formula to solve for the value of x or to solve for the value of position so number one is dimensionally correct so how about number two so x is equal to v times t plus one half a t squared so how do we now solve this one so for number two we have here x is equal to v times t plus one half eighty squared so again punin unit so this is position so meter we have here velocity which is meter per second times second plus so dimensional analysis we do not include the coefficient in solving so just the units of the variable the units of the the numbers or the dimension alone so this will have here a which is acceleration meter per second squared and then time is second wherein we get its square in squared this is just the same as s squared yeah so length we have here another length meter is a unit of length so latin second is a unit of time so we have here another time plus the same in this one so we can use units in dimensional analysis or we can also use the dimensions in order to check whether an equation or a formula is dimensionally correct so since length and then another length always add numbers with the same dimension because [Music] so to describe something this equation is dimensionally correct and we can use this to solve for the value of the position or we can also derive from this equation to solve for the value of any of any variable here that is missing okay so number two is dimensionally correct okay so number three is also dimensionally correct equation so we have v is equal to 80 squared so v is a measure of unit velocity is meter per second so we have here meter per second squared for the acceleration and second four times if you perform the operation we have here meter per second is equal to meter per second so this is a unit of length and this is a unit of so this equation is dimensionally correct so how about for number four so we have your v raised to three is equal to two a x squared so final attention is solved so again you have your v cube is equal to two a x squared so um unity v is meter over second or meter per second and then nakakusha is equal to so we do not include this two so just the units of this of the value so nothing units acceleration is meter per second squared and then multiplied not inches x is measure of if x is a position so one unit is meter yeah and then by square shaft we have here meter cubic meter and then second cube non-second and then equal to so meter times square meters so we have beer cubic meter over second squared dimensions now we have here um and then and then the tournament time this equation is not dimensionally correct so this is dimensionally incorrect so we cannot use this equation to solve for the value of velocity or to solve for any of the value in this equation okay so last item so number four is dimensionally incorrect so number five so t is equal to the square root of two x over eight so let us see the solution so letter sorry letter t surface the letter t sub time is equal to the square root of and on square root of 2x over a square root of 2x over a so time is second so we have here position which is meter and then square root and then acceleration is meter per second squared divided we have your time is equal to 2x over a so again we have your second and then the square root of meter over meter per second squared so it'll we can also write this as the square root of meter times second squared over meter so this means the cancel out symmetry so on along s is equal to second squared so square root of second squared so second is equal to second so this is dimensional unit of time and this is also a unit of time since parago young's a gabilan so therefore this equation is dimensionally correct so this is dimensionally correct so we can use this equation to solve for the value of time so it will dimensionally incorrectly given nothing sorry yeah so as you can see so we can use the we can use dimensional analysis to check whether our equation our formula can be used to solve for the variable so for the physical value of the physical property so for example equation value x the same with this one so also it of velocity and the dimensions are consistent to each other samakabella inside none equation a lot of times in physics you will be dealing with extremely large or extremely small numbers for example the mass of a subatomic particles so this is extremely small numbers and another example would be a distance between the earth a star for example from another galaxy from a distant galaxy so in these cases where we have extremely small or extremely large numbers there is a way on how to express our value so that we would avoid writing a very long sequence of numbers for example if we have this very long sequence of numbers significant figures so how can we express this in such a way now is so in science it is important to familiarize how to write or convert number into its scientific notations because scientific notations is a convenient way of expressing large and small numbers into a simpler manner so it also facilitates comparisons and computations made during measurements so how do we now write a number into its scientific notations scientific notation makes use of a short sequence of number multiplied to some power of 10 raised to a certain degree so it is expressed using the following form so you have your n times 10 raised to n so where the capital letter n is any number greater than or equal to 1 but is less than 10 greater than or equal to 1 but it's less than that and the small letter n denotes the magnitude the order of magnitude or the degree of exponent so it makes a million autoclass for example we have here a value so for example 3.9 times 10 raised to 7. so how do we now know that that this number here um definition or description 3.9 so it is clear that 3.9 is greater than 1 and 3.9 is also less than that so therefore to and the rest of the significant numbers in your value must be written to the right of your decimal so for example if we have here seven nine trees 793 million seven hundred negative million if you would like so one two three four five six seven and eight so from here original place of our decimal nila so now our number is seven point ninety three so young significant digit nothing diva so all the other significant digit must be written to the right of your decimal place left side now significant numbers so therefore so you need to count how many times you moved the decimal places lima so we move the decimal places eight times to the left so nearly again attention eight times so therefore an exponent nothing is eight so you know exponential can be positive so if a number if the original value or original number is greater than 1 the exponent is less than one the exponent is negative is this number greater than one so it is zero three 0.00031 and then we move this decimal places in express nothing into scientific notation so move it one two three four five times so five times to the right negative exponent because zero point zero zero zero zero three one this this number is less than one the original number is less than one excuse me less than one from value you move the decimal places notation original value is greater than one you move the decimal places to the left left side of your number so let's have more examples so let us convert this value into its scientific notation so we have here 158 thousand kilometers so to to convert this into ano into its equivalent scientific notation so we need to move the decimal to the left to the left side of this number so one hundred fifty eight acidity one hundred fifty eight is greater than one so therefore completely done one it will move nothing young decimal so one two three four and five so we moved it one two three four five times to the left so i'm value nothing it's a long insignificant numbers the basis for one times 10 raised to 5 and don't forget to include also the units another example so 0.000 0 0 9 7 8 2 seven liters so let's convert this into its equivalent scientific shock so 0.00097982 liters is less than this is less than one so therefore converting attention to its side direct notation we moved our decimal place to the right of our number hangang s so from this point we moved it one two three four five and six some digits times ten and then one two three four five six times time raised to six and this is negative because the original value nothing is less than one and don't also forget to write the unit so what if we want to write scientific notation back to its original value or back to a standard number so how do we now convert a scientific mutation from scientific relation back to its original but original number or standard number so let us have some examples on how do we write the the scientific rotation back to its original number so number one for example we would like to convert seven point twenty times ten raised to negative seven so first we need to look at the exponent so by looking at the exponent we will be able to tell whether the original number is greater than must be greater than or must be less than but greater than just 1 so since we have here a negative exponent your original number must be great less than once must be less than one so we need to move this decimal place to the left the second button sub this for example from this value for example rotation we move it to the left so we move the decimal place to the left now if the value is is um if the scientific rotation or if the scientific notation has negative exponent so this this original value must be less than one so back to its original value we're moving this to the left side the decimal place must be moved to the left side so times the n exponent so little so 7.20 times 10 raised to negative seven so divided by seven so from here we'll move one two three four five six and seven so we move our decimal place seven times to the left of exponent is negative to convert it back to its original number you need to move the decimal places to the left side of the number so for example mass multiplication for example is a one for example number two 7.20 times 10 raised to 7 so the the exponent now here is positive so therefore since don't zap and convert nothing for example 31 000 for example 31 000 to convert this into to scientific notation diva so we need to move the decimal places to the left so one two three and four so parameter so here if we have here 7 point 20 and the exponent of your multiples of 10 is positive 7 then from this point we need to move this to the right side seven times so from here one two three four five six seven so and these are nine decimal so we have your 4.9 times 10 raised to 12 and then a month number four convert this back into its original value six point twenty three times ten raised to negative nine so you may pause this video and try to answer this problem okay sodito sauna so 4.9 times 10 raised to 12 so since positive you exponent nothing so this must be greater than once so if we write this down back to its original value so from 4.9 we need to move this decimal 12 times to the right because a positive mu exponent is yeah so four billion four trillion nine hundred million volumes so four billion 900 billion 100 billion that is the original value of this exponential expressions of writing a number you will scientification because you'll be able to avoid writing too much zeros or too much number in our original number so for number four six point twenty three times ten raised to negative nine so since this is negative so this must this number must be less than one so your original value is less than one so from six point twenty three sabine negative exponent to convert it back to its original value we need to move the decimal places to the left side so basis so we move this decimal place nine times to the left so one two three four five six seven eight nine so again decimal 0.000 scientific notation okay so how about this one so how about this one how do we convert this or write this in a proper scientific notation so point 435.3 times that is the two so clearly scientific notation this is this number or this number is greater than so this n is greater than 10. scientific notation n times 10 raised to a certain degree and starting scientific notation must be n must be greater than or equal to 1 therefore express negative scientific regions how do we now express 435.3 times 10 raised to 2 into a correct way of writing scientific conditions so step number one 45.3 times 10 raised to 2. so first step is to convert this or express this to its original number so you apply nothing new so how do we express this into its original number so look at the exponent so positive though so therefore from this decimal place to the right side parama convert nothing shut back to its original value so step one malay your way of expressing the the scientific notation step one is convert back to original value so from four three five point three raised to times ten is negative two so since two times since since raised to two and this is positive we need to move this decimal place to the right side parameter value so we move this one so now to write this down back to its um scientific notation just do the steps i showed you a while ago so convert back convert to scientific notation greater than or equal to one per less than 10 so from this point one two three four times to the left paramount correct um correct scientific notation expression four point three five three two significant digits at three so four point three five three times 10 raised to 1 2 3 and 4 raised to 4. so we told you correct way of writing this number into scientific notation so in okay so concept builder meter per second or you miss 2.99 times 10 raised to 8 meter per second for the mass of a strand of hair zero 0.000 zero zero sixty two kilogram or if we write it down into scientific notation again so six point two times ten raised to negative seven kilogram so somebody not independent definition on scientific rotation it is a convenient way of of comparing measurements with other measurements because for example original number is composed of a very long sequence of numbers of course so concept builder so write the following quantities in their scientific rotation so yeah it's 158 kilometers into its corresponding scientific location and yeah convert this back to original number it on number four four point three five two times ten raise to fourteen eight point nine nine zero three times ten raised to negative twenty and eight seven eighty seven point two times ten raised to two so it'll convert it into scientific notation it'll convert this back to its original number okay so you may pause this video and then just resume watching so for number one so the correct answer here is 1.58 times 10 raised to 5 because from this from this value you move not a new number one two three four five times to the left so the positive exponent and this is the number nothing so for number two it will move not the new decimal place one two three four five six times to the right so times 10 raised to negative six liters so number three in a month we have here a value that is greater than one so therefore you move nothing sha to the left you can decimal so one two three four five six seven eight so we move it eight times to the left so therefore incorrect answer is is 8.371 times 10 raised to 8 cubic meter so number four no man so this is less than one so we move the decimal place so to the right so one two three four five six times to the right value yeah so six eight point zero zero four times ten raised to negative six grams per liter so take note class so back to its original value so positive view 4 so therefore amp converts we move it to the right side so back to its original value so we have 43 hundred and twenty ito original valencia so eternal since you exponent nothing is negative yeah so you your original value must be a number less than one so convert and show back to its original value so 20 times the displacement decimal so we have here one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen and then twenty nine of course is eight so eight because if you are going to write this down so number eight so 87.2 times 10 raised to 2. saturn to convert this back to its original so just follow that although express 87.2 times 10 raised to 2 its original values seven eight thousand seven hundred and twenty 87 but 87.2 87.2 times 10 raised to 2 if you want to express this again into correct number i correct significant it's correct scientific notation so you need to convert it back to its original and then convert it back to scientific notation again so nothing is 87.2 times 10 raised to 2. 87 and then it's 8720 and then expressing attention to correct number of significant figures one two three or scientific or significant figures significant figures are digits that are known with certainty so these are these are how we determine whether a value or a number in a certain um a number in a certain value is significant so rule number one all nonzero digits 1.234 zero and five so between four and five and zero so this zero is significant and then five zero seven so this zero is significant so therefore maritime five significant digits are numbered between two non-zero are significant rule number three so zeros to the left of the first non-zero digits are not significant so for example 0.009 excuse me meter per second first non-significant the first non-zero noun number not individual to the left side of this number so these zeros are not significant therefore significant numbers another example first non-zero digit nothing so all zeros to the left of this first non-zero digits are not significant three significant digits so in both examples zeros were just used to locate the decimal so therefore it is not significant so number four rule number four if a number is greater than one so decimal points i significant so it to your number nothing which is greater than one and then decimal point zero so since nasa right side tonight number is this zero or significance so therefore three significant digits are seven point zero zero kilometers so the same in this one so it's four point zero zero five point zero millimeters there are five significant digits so zero zeros placed after the decimal following a number greater than one are used to ascertain the measurement so after our first number that is greater than one places so you know certainty now measurement measuring devices application of an application so if a number is less than one only the zeros at the end of the number and zeros between two non-zero digits are significant so for example dito so meron taylor these are not significant however zeros to the right so less than one new atom value so this is less than one it's a zero point zero zero zero one two zero so zeros to the right of the non-zero are significant so we have here one two this is a non-zero so we have here zero so therefore this zero is significant so three significant digits so the same thing applies so between non-zero this is significant and maple nothing rule number five zero so therefore four significant zeros to the left of the first non zeros were just used to locate the decimal we're just used to locate the decimal places so the first non-zero digit and then zeros to the right are used to ascertain the measurement right so you won't measure uncertainty not measurement rule number six the zeros immediately to the left of unexpressed decimal point are not significant so for example we have here value yeah so four thousand five hundred sodium again a significant decimal point so therefore since expressing decimal point little therefore these zeros here are non-significant decimal point after these two zeros these two zeros are significant hong so this is significant this is significant significant and also this one [Music] significant so decimals and words are used to assert them the number of significant figures sponsored builder number seven so it took one to five and then into you six to ten sir items one to five so determine the product number of significant figures for the following values [Music] and then that is four items one to five you can pause this video and then for items six to ten so let us now answer the concept builder so number one there are six significant digits non-zero digits are significant so we have your one two three four five six non-zeros legit so therefore six significant figures america number two yeah so zeros between non-zeros are significant so therefore you won't significantly just not take so number three seven semester non-zero main and the left side of the first none digit is not significant so then we have here four significant digit so again zeros to the left side of the first non-zero digit is are not we did not express the decimal place here so therefore these two are not significant sodium we have here zeros to the right of the decimal is significant so since this is significant and this isn't significant so between them the the zeros between them or the values between them are also significant so we have here four significant figures so number nine we have here three significant figures so zeros to the left of the first non-zero or not significant and then zeros to the right of a non-zero digit are significant therefore we're retiring three significant figures and then for our last item 0.010 yen so there are nine significant digits not significant this is a significant digit so therefore nine significant figures so how do we apply the correct number of significant figures in calculation so for addition and subtraction you need to look at the least number of of decimals look for the least significant digits after the decimal point so for example after the decimal point two significant digits metro maritime three significant digits significant you need to follow the number the value with the least significant digit after the decimal point so since i told you my only [Music] therefore in expressing this into correct number of significant figures some decimal place so around this off to the nearest tenths place it was 50 points if the value the is value so just recall the rules for rounding numbers so the same with subtractions value with the least number of significant figures to the right of the decimal for multiplication and division among what we follow is the least significant digit so overall hindi along to the right of the decimal pair overalls for example the the neuron by little three decimal i3 significant numbers so what we need to remember is in multiplying and division to write the correct answer or the final answer but if a follow mulan you will list number of significant digits in any factors three factors cubic centimeter or in scientific rotation 4.5 times 10 raised to 4 cubic centimeters so for example not divide so 923 for example divided by four significant digits it is 923 divided by 4 is equal to 203.75 but since unless no need to express this no need to to round this number up so just rotate so 200 you make it so good not indeed following the rules all significant figures so that's all for this video so i hope you learned something and if you have any question you can always send me a message in my messenger fb messenger so see you in our next video thank you