[Music] so hello dear students for today's lesson we will be talking about units at the end of this lesson you will be able to convert units from si to english and vice versa recall rounding off of numbers designate multiples and subdivisions of any unit using prefixes identify significant figures and express numbers in scientific notation we all know that physics is a branch of science but physics is not just it physics is an experimental science where physicists perform experiments to test hypotheses and the conclusions in the experiments are derived from measurements physicists use numbers to describe measurements such a number is called a physical quantity however a physical quantity would make sense to everyone when compared to a reference standard so what are physical quantities physical quantities are those quantities that can be measured these are quantities that are used to describe laws of physics here in this picture we have length mass time electric current temperature luminous intensity and amount of substance yes all of these are physical quantities since 1960 the system of units used by scientists and engineers as the metric system which is officially known as the international system or si units to make sure that scientists from different parts of the world understand the same thing when referring to a measurement standards have been defined for measurements of length time and mass tilde it should be inches feet yard and pounds tilde no it's meters centimeters kilometers and kg in this lesson we will be focusing on these three physical quantities namely length mass and time length of one meter is defined as the distance travelled by light in a vacuum in one 299 792 458 second based on the definition that the speed of light is exactly 299 792 458 meters per second time of 1 second is defined as 9 192 631 770 cycles of the microwave radiation due to the transition between the two lowest energy states of the cesium atom this is measured from an atomic clock using this transition mass of one kilogram is defined to be the mass of a cylinder of platinum iridium alloy at the international bureau of weights and measures today few countries continue to use the british system of units like in the united states the conversion between the british system of units and si units have been defined exactly on the left we have english to metric conversions for both length and weight let us now try to convert some expressions to convert 28 ounce to grams first write down 28 ounce then multiply it by the conversion factor the conversion factor can be found in the table of conversions discussed earlier for this problem one ounce is equals to 28.3 grams in writing the conversion factor notice that the denominator must have the same unit with the number we are going to convert while the numerator must have the unit that we need to convert the given into in this equation we have bounds and grams the given is an ounce so our denominator must be an ounce our numerator on the other hand is in grams because it is the unit we are converting into after writing our equation we need to cancel similar units in this case we need to cancel ounce leaving us grams now multiplying 28 by 28.3 grams we have 792.4 grams sounds easy let's try converting the remaining ones to convert three feet to cm let us write the equation first one foot is equals to 30.5 centimeters according to the table of conversion are given as in feet so we write one foot as the denominator on the other hand we write 30.5 centimeters as the numerator because it is the unit we need to convert our given into cancelling similar feet units we are left with three multiplied by 30.5 centimeters and the answer is 91.5 centimeters let's try another to convert two kilograms to ounce let us look for the conversion factor on the given conversion table nothing is given to directly convert kilograms to ounce but worry not we can use kilograms to grams and grams to ounce let us write two kilograms and use the conversion factor for kilograms to grams is shown then multiplied again by another conversion factor leading us to our desired unit the ounce cancelling all similar units kilograms and grams we now multiply 2 by 1000 and 0.0353 ounce 2 kilograms is equals to 70.6 ounce in certain cases particularly in scientific usage it becomes convenient to provide for multiples larger than 1000 and for subdivisions smaller than in the metric system of measurement designations of multiples and subdivision of any unit may be arrived at by combining with the name of the unit the prefixes on the table so how do i use the prefixes to use prefixes for example 12 times 10 raised to the sixth power we need to look at the table of prefixes and find a factor 10 raised to the sixth power here 10 raised to the sixth power is equal to the prefix mega with the symbol m replacing 10 raised to the sixth power with our prefix we write 12 capital m followed by a small m we read this as 12 mega meters significant figures also known as the significant digits or precision of a number written in positional notation are digits that carry meaningful contributions to its measurement resolution we have rules in determining the number of significant figures first all non-zero digits do count 24 has two significant figures while 3.56 has three significant figures second leading zeros don't count for example zero's in front of numbers and in 0.0025 we only have two significant figures third captive zeros do count capped zeros are zeros between non-zero numbers for example 1502 has zero between five and two thus it has four significant figures also 1.008 has zeros between one and eight thus it has four significant figures fourth trailing zeros do count if the number contains a decimal for example zero's at the end of numbers 100 has only one significant figure because it does not have a decimal point 2306.0 has five significant figures because it has a decimal and 1.00 times 10 raised to the power of three has three significant figures scientific notation is a way of expressing real numbers that are too large or too small to be conveniently written in decimal form it may be referred to as scientific form or standard index form or standard form in the uk this base 10 notation is commonly used by scientists mathematicians and engineers in part because it can simplify certain arithmetic operations the scientific notation is written as shown on the picture it is composed of the coefficient which is a real number with an absolute value between 1 and 10 multiplied by an order of magnitude value written as power of 10. to express numbers in scientific notation the first thing we need to look at is the decimal point remember that the direction of the movement to the decimal point will determine the magnitude and sign of the exponent for the first example 4567.8900 meters the decimal point moves to the left and stops in the middle of four and five the decimal point passed three units to the left giving us 4.56789 the left movement indicates a positive exponent giving us 10 to the power of three for the second example 0.004567 meters the decimal point moved 3 units to the right a right movement to the decimal point indicates a negative exponent giving us 4.567 times 10 to negative power of 3. always remember a movement to the left gives a positive exponent while a movement to the right gives a negative exponent let's answer a sample problem a snail moves one centimeter every 20 seconds what is this in inches per second to answer this first we need to look at the given one centimeter every 20 seconds then look at what is asked we need to convert the given two inches per second let us now write the equation one centimeter every 20 seconds is one centimeter over 20 seconds multiplied by our conversion factor 1 inch equals 2.54 centimeters cancelling all similar units we multiply 1 by 1 and divide with the product of 20 and 2.54 the result is 0.0196 inches per second expressing the result 0.01968 inches per second to scientific notation we can write it as 1.9 times 10 raised to negative 2 inches per second by rounding off we can get 2.0 for sample problem 2 a jeepney tried overtake a car the gp moves at 40 kilometers per hour convert this to the british system feet per second 40 kilometers per hour is our given that we need to convert to feet per second multiplying our given with the conversion factors and canceling the similar units kilometers and m for length an hour and minutes for time we get 36.444 feet per second take note that in converting multiple units we need to convert one at a time in this problem we first converted kilometers into meter then into feet then to convert hours we write one hour on the numerator which is equals to 60 minutes is written on the denominator then converted again to seconds always remember the key to converting multiple units is by writing the conversion factors one at a time now that you have learned how to convert units and express numbers in scientific notation are you ready for a challenge i have prepared five problems that we can solve together for the first problem it takes about 8.0 minutes for light to travel from the sun to earth how far is the sun for the earth the meters take note that the speed of light is 299 792 458 meters per second first writer given eight minutes the question is how far indicating that we are finding an answer with the unit of length looking at our given we need to be able to cancel both units of time so that only the unit of length is left to do this first we need to convert minutes to seconds one minute is equals to 60 seconds multiplying eight minutes by the conversion factor 60 seconds equals one min and by the speed of light we get 143 900 379 840 meters expressing this in scientific notation we get 1.44 times 10 raised to 11 meters for the second problem chloe made 1.5 liters of orange juice 0.75 liters dropped out of the bottle how many milliliters are left the word dropped indicates that something is lost or been subtracted from the given for this we can write 1.5 liters where 0.75 is dropped giving us 1.5 minus 0.75 to determine what the remaining amount of juice is in milliliters we can convert 0.75 liters to ml as shown multiplying 0.75 liters by the conversion factor 1000 ml over 1 liter we get 750 ml now chloe has 750 ml of juice left sounds easy well it really is just easy to solve conversion problems when you know the conversion factors and when you can easily convert verbal descriptions to an equation however if up to this point you are still confused or just looking for more let's proceed to the next problem peter planted 240 kilograms of potatoes and harvested 12 times more of them how many tons of potatoes has he harvested converting the verbal description 12 times more of them or the 240 kilos of potatoes planted we write 240 kilograms times 12. now proceeding to the main problem how many tons of potatoes meaning we need to convert the given unit to ton we write 2880 kilograms multiplied by our conversion factor for ton and kilogram we get 3.175 tonne so peter harvested a total of 3.175 ton of potatoes from 18.2 hectares workers reaped 78.69 tons of grain what was the average yield per hectare of harvested grain converting the verbal description average yield per hectare we can write the equation as 78.69 tons of grains divided by 18.2 hectares we get 4.32 tons of grain per hectare ethan is trying to drink 1.9 liters of water every day given that ethan drank 967 milliliters of water one morning how many milliliters of water should he drink during the rest of the day in this problem we are only asked to subtract 967 milliliters of water from 1.9 liters but since they have dissimilar units we needed to convert 1.9 liters to milliliters first before deducting 967 milliliters from it we write 1.9 liters multiplied by our conversion factor 1000 milliliters equals 1 liter minus 967 milliliters we get 933 milliliters this is all for today if you listened well and have understood everything that we have discussed you can now solve the given problems on page three to four of your physics modules kindly write your solution for every problem and don't forget to enclose your final answers in a box that's it for today have a nice day