a pleasant day to everyone this is mr belty cruz your general physics one instructor for this semester for today's lesson we're going to discuss about measurements a way of life and for our learning objectives for this morning we're going to have the following number one solve measurement problems involving conversion subunit number two express the unit of measurement in scientific notation form for this slide let's have first definitions of measurement the first is numbers which describe living and non-living things second quantitative description of a fundamental property or physical phenomenon third describe such quantities as length weight area volume and time and lastly comparison of physical quantity with a standard let's proceed now to the different systems of measurements so the first one is the local or the obsolete system during the early times class ancient people are using their body parts in measuring so the first one let's subcube it which is the distance from a man's elbow to the tip of his middle finger next is palm which is the width of a person's poor fingers excluding the thumb and they said that one qubit is equivalent to seven palms third is unsha which is the weed of a person's thumb next is the yard which is the distance from a tip of a person's nose to the tip of his middle finger and they said that one yard is equivalent to three feet aside from body parts that they are using in measuring our ancient people also use this such instrument just like the sun dials in measuring time and also in the different parts of the world they have this what we call different system of measurement during the early time and one of the proof of this is in even in our country which have the non-standard unit of measurements so the first one is dhamma or palm which is the width of the palm next is dali or the digit or the width of the finger trade is talam pakhan or foot which the length of a foot next is the mural or the length of the forefinger hak bang or a single stripe dakot a handful used to measure the amount of grain such as corn and balay and aside from it they are using this goosey a jar i use to measure the volume of liquid such as tuba and vinegar ka ing or a container used to measure amounts of hard vested fruits or like main ghost tomatoes and salts and also dangkal from the tip of a thumb and a tip upper middle finger and dipa from a deep upper right middle finger to the tip of the left middle finger peeling which is used in banana tompo usually we can see still in the public market when you want to tell someone how big or how far away something is you need to have a common system for communicating this information there are two most common system of measurement the metric system which is widely used in europe and most of the rest of the world and an imperial or british system or the english system which is commonly used in usa the english system was originally formalized by the british wheats and measure acts in 1824 in order to provide rapidly developing industrial society with much needed consistency however this was a half century after american independence and a system used in the us is based on the earlier 18th century british system two are predominantly the same but they are some different such as the measurements of volume sometimes to watch out for in recipes the british imperial system use units such as pounds and ounces per mass miles yard speed and inches per distance pints and gallons per volume and they have almost more than 20 base units in the metric system was officially adopted as a standardized system of measurement by the french in the late 18th century although it was invented over a century earlier all of the units in the metric systems are in multiples of 10. it means that calculation can be done as decimals so multiples of units can be calculated by dividing and multiplying by 10 and its power this is much easier to work out in your head and it is easily adaptable in all sorts of applications particularly in science and engineering here are some of the grid prefixes attached to the base units the greek prefixes are indication whether the value is bigger than 1 or smaller than 1 which is the base unit so like deci which is actually 1 times 10 raised to negative 1 and yokta which is small y which is 1 times 10 raised to negative 24. and because of the two systems of measurement here are some metric english conversion in terms of blank volume and mass the international system subunit abbreviated as si from the french lesistimate international the unites is the modern form of the metric system it is the system subunit that is general conference on weeds and measures had agreed upon and it is legally enforced in almost all parts of the world and this is based from the physical quantities such as the fundamental quantities and the derived quantities when we are talking about fundamental quantities these are the basic quantities which are commonly measured or can be measured directly using different measuring devices while if we are talking about derived quantities this actually combination of fundamental or other derived quantities and can be determined by using formula the international system subunit of measurements or si units or the official system of measurement used throughout the world especially in scientific applications is based upon the metric system units all as a unit can be formed by a combination of 7 base unit as you can see in this table the fundamental quantities under si units are derived from 7 base units of measurement and each of which are defined in terms of fundamental scientific constant as described in this presentation so let's have the first one the length length is actually the measure of linear distance and has a unit of measurement which is m or meter it is defined in terms of the constant speed of light in a vacuum which is c is equal to 2.99 times and raised to 8 meters per second another si unit of measurement is the mass which can be defined as the object's inertia or resistance to change in motion each si unit is kilogram or kg and this is defined in terms of the fundamental planck's constant h which is six point six hundred twenty four times ten raised to negative thirty four kilogram meters squared per second have you heard the question how long would it take for an object to travel or how cold or hot an object is this pertains to the number three and number four si units of measurements which is the time and temperature when we are talking about time this is a measure how long an object travels and it has a unit of measurement which is second and this defined as the time it takes for a session 1 to 3 atom to oscillate which is 9.192 times 10 raised to 9 times and the fourth one just like what i mentioned is temperature which is measured the average energy per molecule in a substance the si unit per temperature is kelvin this unit kelvin is defined in terms of fundamental boltzmann constant k which is 1.381 times 10 raised to negative 23 joule per kelvin the fifth and number six as a unit of measurement is very familiar to you because when you have your grade 10 science you learn this in your physics class the luminous intensity and the electric current and luminous intensity is a measure of intensity of light the si unit of luminous intensity is candela and it is defined in terms of luminous efficacy of radiation frequency which is 540 times and raised to 12 hertz while electric current is the measure of rate of charge passing through a point and the si unit of electric current is ampere or capital a sometimes it is amp or amp it is defined in terms of elementary charge particle which is e is equal to 1.602 times and raised to 19 column and lastly number seven as a unit of measurement is the amount of substance it is the number of substance containing as many atoms or molecules the si unit for this is mole or mol one unit of substance contain exactly 6.02 times and raised to 23 particles particles can be an ion if it is a charged atom atom or molecules elementary items also known to be the avogadros number here are some of the derived quantities and their s-i unit of measurement these physical quantities are the derived quantities that we're going to show you is based on the fundamental quantities just like what i told you a while ago derived quantities can be solved using formula so just like area which has a unit of m squared volume which is m cube density which is kilogram per meter cube velocity which is meter per second force which is kilogram meter per second squared or newton pressure which is newton per meter squared and acceleration which is meter per second squared so let's apply what we have learned into sample problems so directions convert the following and express the answers in scientific notation if necessary apply this sf rule so for number 1 to 5 you may look for the solution on the attached video on the next slide so let's have this sample problem so directions convert the following and express the answers in scientific notation if necessary apply the sf rule so we have number one so for number one we have 20 meters we need to convert it into kilometers we all know that one kilometer is equivalent to 1000 meters using the conversion factor we can put 20 meters open close parenthesis 1000 meters 1 kilometer why did i put 1000 meters below so that we we can cancel the input measurement meters here so multiplying the value 20 times one we have 20 kilometers over 1000 so we're going to divide it we have 0.02 kilometers but since we are asked to use the scientific notation form of this and it is in decimal form therefore we can say that if we are going to move the decimal point from the here going to the right one two we have two times 10 raised to negative 2 kilometers so that will be the answer for number one let's try sample number two so for example number two we have 50 seconds we need to convert this into minutes so we all know that one minute is equivalent to 60 seconds so therefore 50 seconds open close parenthesis so since this is 50 seconds here we're going to put 60 seconds below the line and we put one minute on top so we have cancelled the second unit so 50 times 1 we have 50 minutes over 60 seconds so therefore if we're going to simplify it 50 divided by 60 we have zero point 83 minutes but since it is one as f based on the given that we have we can say that it is 0.8 minutes all right and in the scientific notation eight times ten raised to one minute so let's have example number three so we have here 100 megahertz to be converted into hertz hertz is the unit or the base unit for the frequency just what you have learned in your when you were in great than in waves so we all know that 1 megahertz is equal to 1 times 10 raised to 6 hertz based on the conversion factor that we have in the slides that i gave you a while ago so therefore using the conversion unit of measurement so 100 megahertz open close parenthesis one megahertz is one times ten raised to six hertz so cancel out at megahertz as a unit of measurement we have one times ten raised to 10 hertz so that's the answer for number three so let's have number four 45 micro hertz converted into millihertz so we all know that one micro hertz micro is equivalent to one times and raised to negative six and you're immediately one melee is equivalent to one times n raised to negative three so using the conversion unit of measurement 45 times one we have 1 times n raised to negative 6 micro hertz opening those parentheses so 1 times 10 is negative 6 micro hertz over one times center is negative three milli hertz simplifying the two we need to remove this unit of measurements so therefore we have 45 times one exponent negative three we have 0.045 my milli hurts since we are following as a rule and it should be in scientific notation therefore we need to move the decimal point so from here we need to move to the right so one two so we have 4.5 times 10 raised to negative 2 micro hertz do not forget to box your answer if you are going to solve something in the sample problems that we're going to have also so let's have sample number pi which is 15 meters per second convert into kilometers per hour but first let's have the conversion unit of measurement here so we all know that one kilometer is equivalent to 1000 meters and let's have also one r is equivalent to 3 600 seconds so let's convert using the conversion factor 15 meters per second open close parenthesis so since we have two units to be converted we need to use also two conversion factor also so first since this is meter we need to put 1000 meters here which one kilometers on top and seconds we have 3600 seconds over 1 hour cancel the unit to be cancelled so therefore 15 times 1 times 36 we have 54 thousand kilometers over 1000 rs so simplify it by dividing the 54 000 kilometers by 1000 or we have 54 kilometers per hour and following the s app rule so we have to ask f okay but we need to convert into scientific notation so therefore we have con move it go into that so 5.4 times and raise to one kilometers per hour okay so aside from the one to five that we have we have here another sets of sample problems and you may look for the solutions on the next slide so let's try to solve this what if the unit of measurement it is squared so therefore for example let's have number one 55 meter squared convert into feet squared so we all know that in a base unit of measurement one meter is equivalent to 3.28 feet but since there is a square on both of the unit of measurement what are we going to do is we need to square the equivalent value of one meter into feet so therefore one meter squared is equivalent to 3.28 squared is equivalent to 1.08 times 10 raised to 1 feet squared so since we already have this we can now proceed to the conversion so 55 meters squared open close parenthesis for the unit conversion so we have 1 meter squared is equivalent to 1.08 times 10 raised to 1 feet squared so we can now cancel the unit so 55 times 1.08 times and raised to 1 feet squared is equal to 5.92 times 10 raised to 2 feet squared but since we only have two sf here so therefore the answer will be 5.9 times 10 raised to 2 feet squared so that will be the answer for number one okay let's try to solve number two which is an example of a derived unit of measurement so we have here 120 meters per second squared which is the unit for acceleration converted to kilometers per r squared so what are we going to do first we need to look for the equivalent of each unit of measurement so we all know that one kilometer is equivalent to one thousand meters and one hour a while ago is equivalent to three thousand six hundred seconds but if you will notice in our given the second e is squared so therefore we need to square it also both sides so squared not then so we have one r squared is equivalent to one point thirty times ten raised to seven second squared so we can now proceed to the conversion so 120 meters per second open close parenthesis so we have squared so 1.30 times 10 raised to 7 seconds squared over 1 r squared then on the other side we have 1000 meters in one kilometer so cancel the unit of measurements so we have 120 times 1.30 times 10 raised to 7 times 1 we have 1.59 times 10 raised to 9 kilometers over 1000 r squared so 1.59 times times raised to nine squared divided by one thousand we have one point fifty six times ten raised to six kilometers per r squared since we have 2sf so we need to follow the sf rule so we have 1.6 times 10 raised to 6 kilometers per r squared so that will be the answer for these sample problems let's identify which of the following children are not allowed to write the surf dance so for the solution you may look for the video attached to the next slide let's try to solve this sample problem so children below 3 feet are not allowed to ride the surf dance who among the following will not be allowed to ride boy a who is 0.75 meters boy b who is 150 centimeters in height or c boy c who is 50 inches in height so let's try to solve so letter a first so let's have 0.75 meters so we all know that one meter is equivalent to 3.28 feet so 0.75 meters up in close parenthesis 1 meter is 3.28 feet cancel the meter unit we have so press in your calculator 0.75 times 3.28 we have 2 0.46 feet so that is the height of boy a let's proceed with boy b boy b who is 150 centimeters in height so we all know that one foot is equivalent to 30.48 cm so let's solve so 150 cm open close parenthesis 30.48 cm is equivalent to one foot cancel so 150 times one divided by 30. 48 we have 4.92 feet and for letter c we have boise who is 50 inches in height so 50 inches convert into weight we all know that one foot let's give it to 12 inches so therefore 12 inches below 1 put on top so we have 50 times 1 divided by 12 we have 4.17 feet so therefore among the three the only child who is not allowed to ride is boy e because his height is below 3 feet which is 2.46 feet okay