hi everyone the metro conversion problems really got lost in the shuffle this week with all of the introductory material so i want to make a separate video on metric conversions if you understand the metric prefixes in the metric base units you can skip this beginning part and just go straight to where i start working the problems if that's the only part you need but i encourage you to watch the whole thing if you really need help with everything so as we discussed in class in the metric system we can measure volume length and mass or weight using the same exact term every time so rather than the english system of measurement for volume where we have teaspoons tablespoons cups pints quarts gallons and there's no direct conversion between those we have to memorize a lot of things everything in the metric system is units of 10. it's a 10 based measurement system for volume the base units or standard units are always liters and the abbreviation for that can be a capital l or a lowercase l and i'm gonna make it loopy so it doesn't look like a one if you do it like this it obviously looks more like a one length is always meters which is an m and mass or weight is always grams which is a g to make this bigger or smaller we use a prefix and that prefix means the same thing whether we're talking about liters meters or grams it means the same thing every time so we wouldn't say we have a thousand grams we would say we have a kilogram we wouldn't say we have 1 100 of a meter we would say we have a centimeter so let's quickly talk about those metric prefixes again if you don't need this part skip it and go to the calculations i'm going to draw sort of a number line so if these were my base units or my standard units okay meaning one liter one gram or one meter to make the base units bigger the only one you need to know is kilo abbreviated with the letter k and it's 1 000 times bigger than the base units okay so it would equal one kiloliter is going to equal 1000 liters one kilogram equals 1000 grams and one kilometer equals 1000 meters that's the only one for this class that you need to know for getting bigger there are obviously more if you look at the lab exercises there's a whole complete chart of all of those metric prefixes for getting smaller than the base units we're going to use different prefixes so getting smaller and then we're going to get smaller and then smaller again the first one is going to be centi abbreviated with the letter c and centi is 1 100 of the base units and remember we talked about there are two ways you can express this and i'm going to use both ways first though on this chart i'm going to just use the one one hundredth so one centiliter is one one hundredth of a liter one centigram is one one hundredth of a gram and one centimeter is 1 100 of a meter so again means the same thing regardless of what we're talking about the other way though that we could express that is if a centimeter is 1 100 of a meter it means it takes 100 centimeters to make the hole okay so i don't have a meter stick i just have this small metric ruler but if this was an entire meter each one of these is a centimeter so this this number one here that's one centimeter and it takes 100 of those to make the whole meter so each one each one is 1 100 of the whole that means it takes 100 of those to make the hole those are saying the same thing so we could also say that rather than saying one centimeter is 1 100th of a meter we could also say 100 centimeters equals 1 meter that's saying the same thing and that's important when you start doing your calculations because sometimes it's going to be easier to use the whole numbers instead of the decimal one of these will make more sense to your brain than the other one go with whichever one you could more easily remember some people it's easier to remember that the centimeter is a fraction of the whole for some it's easier to remember that it takes a hundred of the little ones to equal the big one okay millie is the next one and that's an m and that's one one thousandth so it takes a thousand of the millies to equal the whole so here we go one milliliter is one one thousandth of a liter kind of running out of room here the other way we could say that is it takes 1 000 milliliters to equal 1 liter those are saying the same thing so in other words it takes a thousand of the small ones to equal the whole so each of the small ones is 1 1000th of the bigger one and then the same thing would go for meters and four grams i'll just write that down here so if one milliliter equals one one thousandth of a liter one milligram is one one thousandth of a gram and one millimeter is one one thousandth of a meter okay and again we could also say it takes one thousand millimeters to equal one meter it takes 1 000 milligrams to equal 1 gram those are saying the same thing and then finally the last one you need to know is micro micro is 1 1 millionth and so that would be way over here micro it's one one millionth it's abbreviated with the mu symbol it's going to be five zeros and the one and again i'm going to write that somewhere else but i really should have moved kilo over to the right a little bit more now that i'm looking at this but i just wanted you to see this number line of getting smaller and then getting smaller and then getting smaller and here we're getting bigger so i hope that makes a little bit of sense this messy drawing but let me write micro down here okay so micro is one one millionth so five zeros after the decimal what that means is 1 microliter is 1 1 millionth of a liter another way to say that is it takes 1 million micro liters to equal 1 liter that's very small if we were in person for lab you would be using a micro pipette which incidentally is part of the basic measurement techniques part of the lab this week and when you look at that micro pipette imagine that that little tip holds millionths of a liter that's very small when you get into microbiology if you go on to take it or if you take anatomy or physiology a lot of things you look at under the microscope you're going to measure the size of those cells or cell organelles in micrometers one millionth of a meter those are very very small so it takes one million micrometers to equal 1 meter it takes 1 million micrograms to equal 1 gram and again the other way we can say that is we could say that 1 micrometer is 1 1 millionth of a meter i always have to count the zeros to make sure i did it right and one microgram is one one millionth of a gram those are saying the same thing we're going to now use these conversions turn them into fractions and use that as a method for converting from one unit of measurement to another okay so if you've skipped ahead this is where you want to start working the problems i'm going to give you a bunch of sample problems well not a bunch i'm going to give you several practice problems to use as examples when you're when you are working the problems you know in math it's all about seeing the pattern the more you do it the more likely you are to see the pattern once the light goes on and you see the pattern then you're just going to follow that same pattern for every single problem and it just takes a lot of practice these kinds of things take practice you weren't born knowing this don't feel bad if it takes you some considerable amount of time to figure this out i know that there's anxiety about math in general you can do this and i'm here to help you so if you're still struggling after you get through these sample problems on the video i i'm going to post some additional sample problems but please come see me in my office hours and let's work as many problems together as you need until you start seeing that pattern these are very important to understand so my first problem that i'm going to work for you how many milligrams are in 22 grams okay another way we could word this problem incidentally is we could just say something like convert 22 grams sorry okay why is my eraser suddenly not working sorry about that convert 22 grams to milligrams would be another way of saying that so you always start with what you're given in this case it's 22 grams and i want to convert it to milligrams and i'm going to do that by multiplying by a fraction of equivalent numbers what are my equivalent numbers i'm always going to write those down so i make sure i don't make a mistake okay so i know by looking at my milli i can either use this one okay or i can use this one and i'm going to make that into a fraction i personally like whole numbers but i am going to work it both ways for you so you can see that you come up with the same solution okay so i can either say there are one thousand milligrams in one gram or i can say one milligram is one one thousandth of a gram those are saying the same thing i'm going to use this one first okay so i need to turn this into a fraction one of these numbers is going to go on top and one's going to go on the bottom the way i determine which one goes on top and which one goes on bottom i'm trying to cancel out grams so that means i need to divide by grams so no matter what my grams need to go on top which means my milligrams go on i'm sorry did i just say my grams need to go on top i should have said grams go on the bottom right where i've written it so grams have to go on bottom so when you divide grams by grams they cancel out now i just need to fill in my numbers and these numbers don't change okay it has to be a thousand milligrams equals one gram so one thousand milligrams one gram now if i divide grams by grams they cancel out i'm in milligrams and this question says how many milligrams so my answer is going to be in milligrams you always have to include your units in the problem and in the answer and you must set it up this way to get credit on the exam on the lab exam if you don't show your work this way you will not get credit even if you got the right answer now i just do the math and remember you multiply by what's on top and you divide by what's on bottom so it's going to be 22 times 1000 divided by one i can skip the divided by one step because that gives me the same solution so it's 22 times 1000 which gives me 22 000 milligrams so there are 22 000 milligrams in 22 grams those are the same thing so converting 22 grams to milligrams 22 000 milligrams in in 22 grams if i decided to use this equation instead i'm going to do the same thing i'm going to start with my 22 grams i'm going to make a fraction my grams have to be on bottom in milligrams on top why because i want to cancel out grams and if i divide grams by grams they cancel out one milligram on top one thousandth of a gram on the bottom and if i divide 22 by .001 i get 22 000 and it's milligrams so that's a very basic one-step conversion you need to always write down your equivalency make it into a fraction decide which way to flip the fraction which number is going to go on top in your numerator and which one's going to be on the bottom in your denominator okay let's do another one how many meters are in 7.4 kilometers again we're going to start with what we're given 7.4 kilometers i'm going to multiply by a fraction that converts kilometers to meters and i can go back to my kilos here and here's my kilometers one kilometer equals 1 000 meters so i'm gonna write that down here oops okay so one kilometer equals 1 000 meters this becomes my fraction i just need to decide which way to flip it and i need to decide does the 1000 meters go on the top or the bottom does the one kilometer go on the top or the bottom in this case i want to cancel out kilometers so my kilometers need to go on the bottom and my meters need to go on the top now i just fill in my numbers one kilometer one thousand meters and i multiply seven point four times a thousand and again technically it's divided by one but you don't need to do that step but most importantly my kilometers cancel out and i'm in meters and my question says how many meters so i'm already at the solution with just one step okay so 7.4 times 1000 is going to be 7 400 meters okay that's a pretty basic one just one step again the trick is write down your equivalency make it into a fraction and if you need to work it out you can use your cell phone calculator and if it's just a one step problem it shouldn't be that difficult sorry my calculator is right here one second and i just want i just want to show you that on your calculator if it's a multi-step problem you don't have to go through multiple steps so i would just on this one is just one step so i'm just going to go 7.4 times 1000 and that gives me 7 400. but again you can do that in your head that part okay now we're going to get to one where we need more than one step to complete the problem and this is where it gets a little bit trickier for some students okay if one quart equals 0.95 liters so it's almost a full liter how many quarts are in 2000 milliliters okay first question how do i know this is a multi-step problem the reason i know this is a multi-step problem is because the equation that i'm given for equivalency here 1 quart equals 0.95 liters i want to convert to quarts but my conversion factor is between quarts and liters and i'm starting with milliliters in order to use this piece of information i need to first get from milliliters to liters okay so i need to convert from milliliters to liters and how am i going to do that i'm going to do that because i know there are 1 000 milliliters in one liter so i can turn this into a fraction and i can use that to convert from milliliters to liters first so i'm going to start with what i'm given 2000 milliliters and to convert to liters i'm going to use this as my fraction what do i want to put on the bottom i want to put on the bottom whatever i'm trying to cancel out in this case i'm trying to cancel out milliliters so my milliliters have to go on the bottom which means my liters have to go on the top milliliters divided by milliliters will cancel out milliliters now i just put in my numbers one thousand milliliters equals one liter so that means i'm going to divide by a thousand but i don't do that yet i'm going to set up my next parentheses right next to this one and now i'm going to use this equivalency i'm now going to go from leaders to quarks because now i'm in liters okay now i can go from liters to quarts i want how many quarts so if i'm trying to cancel out leaders my leaders need to go on the bottom and my quarts need to go on the top liters divided by liters cancels out and now i'm in quartz and this says how many quarts okay now i'm in the right units i just have to write in my numbers one quart sorry oh my gosh 0.95 liters so in this case it's going to be 2 000 divided by a thousand divided by 0.95 i don't hit equal in between the way i'm going to punch this into my calculator again it's technically 2 000 times 1 divided by a thousand times 1 divided by 0.95 but you don't need to do the times 1 because you end up with the same answer so the way i put this in my calculator is going to be 2 000 divided by 1000 divided by 0.95 equals it comes out of my calculator to be 2.105 i could round this to 2.10 or just 2.1 but either way you want to include the units so i'm going to say it's 2.1 quarts again the way i knew it was multi-step is because this first conversion factor i've been given uses different units of what i'm starting with so now i need to think okay i'm starting with milliliters how can i use this conversion factor oh i can convert milliliters to liters and then i could use it okay we don't want to try to convert milliliters to quarts i would try to convert metric to metric okay and then i can use that piece of information i'll work one more for you i'm just going to make this one up and this is very similar to one that's in the problem set okay so if one inch equals 2.54 centimeters how many inches are in 12 meters this is another example of a two-step problem how do i know that because i'm starting with meters but my conversion factor to inches uses centimeters so i need to have somehow get from meters to centimeters first how do i do that i do that by knowing that there are 100 centimeters in one meter okay i could also know that oops sorry i don't like that on this side i could also do that by knowing that one centimeter is 1 100 of a meter again you could use either one of those i'm just i'm going to use whole numbers for this one so i'm going to start with my 12 meters and i'm going to convert to centimeters so that i can use this one next okay i want my meters on the bottom so this becomes my fraction which way do i flip it well i want meters on bottom so meters cancel out centimeters on top so that means it's going to be 100 centimeters over 1 meter now i'm in centimeters so now i can go centimeters to inches and i'm going to make this into a fraction what do i want on the bottom i'm trying to get rid of centimeters so centimeters have to go on the bottom and inches go on top centimeters cancel out sorry this is hard to see now that i've been drawing on it this is 100 right here my one inch goes here 2.54 centimeters okay again it's okay to put a number on the bottom it doesn't always have to be one sometimes you're gonna have a number that's not 1. this says how many inches and now i'm in inches so now unit wise i know i'm there so now i just need to do the math and again the way i'm going to put this into my calculator is i'm just going to go straight across i'm not going to solve in between so i'm going to say 12 times 100 i don't need to divide by 1 or multiply by 1. so it's going to be 12 times 100 divided by 2.54 and i'm going to punch that in all at once 12 times 100 divided by 2.54 equals 472.44 and my units are inches so i hope that helps please do not hesitate to come to my office hours if you have additional questions but i encourage you to try to work through as many problems as possible so you start and the more you work through the easier it will be but again you weren't born knowing how to do this please don't be frustrated or discouraged if you don't get it the first few times please come see me or work through some problems together and then i encourage you to work as many of the practice problems as possible i will also post the key okay but i encourage you work the problem first and then look at the key only to see if you got it right don't use the key to study because you won't learn as well that way okay thanks