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Metric and Unit Conversion Lesson Sept. 1 & 2

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hello AP Physics is mrs. Comstock and after taking a look at your quizzes that you took yesterday I decided we needed a little bit practice on the metric system you've been giving a handout and you're going to follow along with that hand out as I do this video Lesson after the video you're going to be given another practice sheet of which will be homework and we're going to have another quiz on Thursday okay let's go ahead started the top prefix the shown are the prefixes that you are expected to have memorized and be able to convert between without using a reference table you can remember this order which is given from biggest to smallest by the saying King Henry dance merrily down Center main now noticed the base units that are given could be meters Sam's or leaders but that's saying worked better by using the m in meters but you can exchange the meters for grams or liters any of these metric problems if you take a look at the prefixes table that are shown here this is the same next table that's going to be given on the AP test and I put it on your hand out for reference today  let's go ahead and do a couple examples just determining which value is the biggest so you look at number one under which is bigger I'm asking you which is bigger a hectometer or a meter this you can use the top  units that I've given you and if you take a look here is the Hector and the Miller  is there so anytime you have a prefix of Hector that it'll be larger than anything the right of Hector in that list so a hectometer is larger than a millimeter number to a Pico or a nanometer now if you take a look the pickle meter and the nanometer are not on those basic pretty is that I've asked you to memorize so you need to look at the prefix chart and if you take a look we have a prefix of Pico here  and Now they're so if you can take a look Nano is 10 to the negative 9th while Pico is tuna negative 12 so a nanometer is larger than a picometer  yeah using the table giving on your hand out where the prefixes we're going to do some more converting so the second set of questions asked you to answer the following converting to the first question were going to ask how many grams are there in 1 dekagram so even though you can move decimals along I want to show you how to set up a conversion factor to do this type of question so if I have one dekagram I'm going to put One Cop capital D for Deca and then Graham notice a dekagram does not have a slash rapper or divided sign so I'm going to put that over one  no I want to know how many grams that so I need to get rid of the dekagram  so I'll set up another fraction and since dekagram is in the numerator on the top to put decagram  in the denominator at the bottom  now I want to know how many grams are in a dekagram so the unit of gram is going to go on top hopefully using that article along the top you can see the dekagram is bigger than the base unit gram so we're going to make the decagram one we're going to ask the question how many dekagrams are in one gram now I'm going to go back to the previous slide in can you how I use. Chart at the top to help get this answer so if I look top and I'm going to want to know how many grams are in a dekagram since dekagram is the biggest I'm going to the number one under the DECA and now I'm going to fill in zeros for each column until I get to the column that looking for that since the gram is the base unit I will only put a zero underneath that column so now I can determine that in decagram there are going to be 10 grams so in one dekagram there are 10 grams I can cancel out the dekagrams multiply cross the top / the values on the bottom and my answer will be 10 grams  long the same lines how many seconds are in a year so if I want start out with a year and I wanted to know how many seconds by first fractional V1 year and since there is not division sign in my unit I'll put it over 1  well I need to get rid of a year  and I want to go to a second but I have no idea how many seconds are in a year but I do know how many days are in a year so I'm going to go to the next unit in someone have days I need to make this fraction equal to one so I'm going to go to the largest unit which is a year  and in one year I need to know how many days hopefully we all have that memorized and it'll be 365 place we can now cancel out the year but since I have the unit left of days and I want seconds I need to set up another conversion Factor  I want to get rid of days so since days is in the numerator here I'm going to put days in the denominator little cancel out and the next convenient time increment will be hours since the day is the largest I'll say one day and we should know how many hours are in a day so we'll put 24 hours my days will cancel out  still looking for seconds but the units I have left are our so I want to get rid of hours and now I can go to seconds  and in one hour there's 3600 seconds remember there 60 min in an hour and 60 seconds in a minute so 60 * 60 is 3600 my hours are canceled out now the only unit I have left is seconds so I can do that math  plugging in calculator I now have 365 * 24 * 100 and obscuring * 20 4 * 3600 and we get the value 31536000 seconds but that's a lot of significant figures but since I wasn't given any to start with that's the answer that we will  stick with the last one are going to ask how many centimeters are in a meter  so if I start out with one meter  I put that over one I would like to get rid of the meter and I want to go centimeter  going back to my  King Henry danced merrily down Center Main I can use this reference as well and we're asking the question how many centimeters are in one meter one meter is my base unit and since since meter is here and centimeter is here my largest is going to be the meter and I'm going to fill in in each column one for death I-10 for Sentai and that'll tell me there are 100 centimeters in one meter so in one meter there are 100 centimeters by meters cancel out and I have my answer of 1 centimeter  not realize that the first question here in the last question here you could have gotten by simply moving the decimal and or using the chart on the stage but I wanted to show you how it looked setting it up as a conversion because we'll be doing a few more of those a little later  if you need a little more to copy this down please ask to pause the video for a few minutes  okay now we like to use Texas to correctly Express the quantities given so what we need to do is go back couple slides in reference the text table that is provided on your sheet  so the first question asked hate to correctly Express 5 x 10 to the third grams so I need to go to my table and find out what prefix means x 10 to the third this Earth is right here and we notice that the prefix kilo has the symbol K represents 10 to the third so I can represent this as five  kilograms you have to have the 5 and you have to have the kilo in front of the grams all you've done is substituted out the x 10 of the third and replaced it with the symbol that represents kilo so let's take a look at the second one 9 X 10 to the negative 6 meters we know we're going to have a quantity of 9 but we need to get rid of that x 10 to the 6 looking at your table 10 to the negative 6 is here and it's by the prefix micro and has the symbol that which is a Greek letter and do not confuse it with an m and when we go back we can now take the x - -6 out replace it with the symbol micro and we're still in meters you have to have the units to make sure that the expression is expressed the same as what you started and finally 3 x 10 to the negative 12th we need to look at our table for what 10 to the negative 12 is and to attend the negative 12th we've seen it already today is Piko represented with lowercase p  so we need to put the three substitute out the 10 to the negative 12 enter the Piko and then leaders so use a capital l for leaders  that's how you use a prefix to represent a quantity that might be 10 in scientific notation we also need to be able to go backwards using this method as well so if I was told you had 5 Graham's which what we have here and I wanted to go in this direction you take out the kilo which is represented with x 10 to the third can you place it in instead so you have 5 x 10 to the third same thing here if we were going backwards we would find out what value represents micro and we would see it was x to the negative 6 so you would take the micro lap and inner the X 10 to the negative 6 and again with the Geico you would find out that FICO represented 10 to the negative 12 so you would have substituted out Piko and entered 10 to the negative 12 please make sure that you can go either way when using the prefixes that to express the quantities or using the quantities and determine what the prefixes are  no I just have this up again so that I can reference it in a few moments we're going to do a little bit do a few more conversions that are going to be a little bit more challenging so watch what we're going to do and hopefully it'll be a little bit easier when you do your own we're going to convert from 25.0 mm into decameters per second  so we're going to take original quantity which was 25.0 mm but noticed now we have a dividing science we have to put that over hours and we're going to convert from millimeters to decameters and we'll do that first and then we'll come back and get from hours to seconds so we're going to set up a conversion factor and we need to know how many millimeters are in a decameter or how many dekameters are in a millimeter if we look back at our table we will see that a decameter is definitely bigger than a millimeter so we're going to make the decameter get the number one we're going to fill in zeros in each column until we get to the millimeter and that will tell us if there are 10,000 mm in 1 decameter  so if we put millimeter on the bottom and decameter on the top we just determine that 1 decameter there were 10000 mm now are millimeters cancels out and we have the appropriate unit on the top play want to convert from hours to seconds so we set up another conversion factor and since our was in the denominator now we're going to put our in the numerator and we can straight 2 seconds because we already know that in one hour there's 3600 seconds my hours cancel out my only y what's that I have left is decameter on top and seconds on bottom so we can pull out our calculators and we're going to multiply the values across top multiply the values across the bottom and then divide  and that will give us 6.944 x 10 to the negative 7 Deka meters per second but notice that since we only had 3 sig figs Pacific to the Atlantic that 0 is we need to make sure that our answer has three significant figures so we would say 6.94 x 10 the negative 7th Deka meters per second is our final answer  II 7248 seconds since there's not a fractional put that over one I want to get rid of seconds help so I can win in that denominator I want to go to hours and went in the numerator and in one hour there's 3600 seconds I have the desired unit on top so now I'll do that math which will be 7248 / 3600 the answer thumbs up to 2.0 133 repeating using significant digits my answer should only have half for sig figs so to .013 hours is my final answer if you need a little bit time to copy this down please ask to stop the stop the video and start it back up when you are finished  we have another conversion factor here 85 km per hour and how many millimeters per second we're going to set up our notice we have the dividing sign so over ours we also want to convert from kilometers to millimeters and we went to also convert from sec I'm hours to Second so it's going to take least two steps convert the kilometers first since kilometers is a numerator kilometers goes in the Dominator to the millimeters  if you go back to that original notice that here we've got a kilometer and here we have the millimeter so a kilometer is definitely the largest cuz we're going from largest to smallest from left to right we're going to put a one underneath the kilometer and then we're going to every single column  until we get to the desired prefix and that will tell us that there are 1 million cuz there's Zero's they're 1 million mm in 1 km  so in 1 km 1 million millimeters I can get rid of my kilometers have the desired unit of millimeters on top now all we have to do is get rid of our hours which goes on the top so it cancels out seconds on the bottom and in one hour 3600 seconds  we're left with that units of meters per I'm sorry millimeters per second so now we can do the math you have 85 * 1 / 3600 and we get 23000 611 but since we had two significant figures when we start with 85 we need to round this to 24,000 millimeters in a second can you deposit to write it down please stop the video  now we need to take this these numbers out of scientific notation what you need to realize is that if 10 to the negative 5th that must be a small number we're going to meet need to move the decimal 5 places so we're going to start zero point and since is a -5 for the desk for the prefix that means were going to put four zeros in front of it and then fine 527 noticed that we would have had to have moved it one two three four five if we wanted in scientific notation 5.27 x to the negative 5th so there was four zeros in front of it to make that work and please don't to put the units so to take it out of scientific notation you would have had 0.00005 to 7 the bottom represents a very large number 6.375 6 x 10 to the 7th so to take this out we're going to have our sex and then now we're going to need to start realizing that the three is actually doesn't place the 7th decimal place at 6 and I've already used for of my decimal places so now I need three more zeros in grams you can always can work by going backwards one two three four five six seven seven places to the left would have indicated direct x 10 to the 7th prefix  so there is our final answer let's work the other way and put numbers in scientific notation here we have a very large number that we would be harder to ride zeros with and we're going to take the understood decimal and we're going to move it so there's only one digit to the left of the decimal and please remember that can you do this you can to the correct way is to make sure it's only one digit so we have 8.9 and there was play two significant figures in this large number so there's only two significant figures in my face number  times 10 why we need to determine how many places to move the decimal at so we went 1 2 3 4 5 6 7 8 9 1011 so we have a positive 11 I do not have any units here so that's my final answer 8.9 X 2 to the positive 11s  let's take a look at the next one will want to move the decimal so that is between the 5 and the two still have 5.230 why do we need that 0 there are four significant figures in this number if you have the Pacific to the Atlantic going to count in that direction and those four digits are significant  math times 10  and we move decimal 1 2 3 places to the right so we'll have a -3 correct answer 5.230 x 10 to the make it up third and lastly 15.1 the decimal CR only going to one place to the left so I have 1.5 1 * 10 + since I moved it to the left it's a positive one  if you need some more time Fast Stop the video  now the next thing we're going to do is to just do some math calculations and determine how many digits at our answer should be rounded to if we multiply 23.24 X 1.0 to 3/8 we're going to get the 23.7 93112 but we will need to use significant digits to find out turn around this you are going to have four significant figures in this number and 5 significant figures in that number we always side with the smallest value Tsar answer can only have four significant digits so we'll have 3.7 and 9 stays at 9 since the 3 after it will not cause it to round up and that's our final answer now let's take a look at so sorry let me back up and we were adding that instead of multiplying  I apologize let's take a look on this one we would have had 23.24 + 1.0 to 3/8 and when we add those together we would have gotten 24.26 3 8 but we look at decimal places here when are two decimal places in this number but there are four decimal places here so we go with the lowest and we want our answered only have two decimal places so our final answer will be 24.26 VI not round up now we have a multiplication division and if we multiply 1235.40 by 520  will get the answer 64.2 408 now this has one too 3456 significant figures and this one has three significant figures so we want around our answer to the lowest value which is 3 our final answer we 64.2 sense R2 will not Roundup please ask if we need to stop the video to make sure this is copy down  well that wraps up this video sorry about that mistake you're not going to be getting a handout to work on I'll be available tomorrow during a mega lunch to give you the correct answers and help you if you need any hope you have a nice day good-bye

Uploaded by Nicole Comstock.

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Metric and Unit Conversion Lesson Sept. 1 & 2

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