How to Convert Units of Measure!

0:00Alright, let's talk about how to convert units of measure.

0:04Maybe the concept that is used the most in any science class because almost

0:08every single problem is going to require you to convert units in chemistry

0:14physics biology kind of whatever converting units is a big one that never

0:19leaves once you learn it and you'll see lots of different ways on how to convert

0:25units and because it's kind of just using fraction math there are lots of

0:30different ways to show it lots of ways to draw brackets or different things to

0:34help people remember it and the way that I'm going to go over today is kind of

0:38the longest way possible this is the anti shortcut way which sounds annoying

0:44but I think that this is the way that fundamentally explains it and if you are

0:49struggling and if every time you have to convert units you just find yourself

0:53flustered and lost you don't know which number to pick or where to put it this

0:57is the way that really explains that so this is not the way that's going to get

1:01done in like a minute but this is the way that's going to help you understand

1:05and even if you don't know what's happening as long as you carefully

1:09follow all of these steps you're going to get the right answer so if you're

1:13just starting out or struggling this is the way for you and so let's start we'll

1:17be doing our practice problem how to convert 16 centimeters into meters and

1:22so step one is to identify your conversion ratio and so in every

1:29conversion problem we're going from one unit to another and there's always some

1:33ratio that's going to connect those two and this is kind of how to find this is

1:38kind of more of an introduction on the metric system or something else

1:41so we're just going to start with assuming that you know how to find your

1:44conversion ratio for this problem and so that means that we have to know the

1:48relationship between centimeters and meters and so that relationship is that

1:55a hundred centimeters equals one meter and so this is our conversion ratio

2:04that's step one we're done we know that this is how centimeters and meters

2:08relate to each other so step two write your conversion ratio as its

2:13two possible fractions and what I mean by that is that your equal sign is now

2:19going to become your fraction bar and so for this are two possible options are

2:27100 centimeters over one meter and then our other option is one meter over 100

2:39centimeters and so I made both of them because I don't know which one I'm going

2:43to need yet all I know is that I have my conversion ratio and this equal sign is

2:50now going to turn into a fraction where either one could be on top so that's

2:55always what you're going to do is just make these two different fractions with

2:58both opposite options on top and so now step three draw your given number as a

3:05fraction including units and this is really important because every number is

3:10secretly a fraction whether or not it shows it and so the number that we got

3:14in the problem is just written like this 16 centimeters and now we're going to

3:20draw that as a fraction and so what that means is that if there's no fraction

3:24like seen immediately it means that this is secretly a numerator and so if it's

3:30secretly a numerator then when we draw it out it's going to be like this 16 and

3:35centimeters very important are both on the numerator and our denominator is

3:39just one because remember that if our denominator is one then really what we

3:44see on the numerator that just is our total answer and so this step is really

3:49important and never drop the unit's all students want to drop units it's just in

3:54their blood don't do it especially in these problems we're converting units

3:58make sure that you know that you're centimeters is on the numerator it's

4:02very important okay great so now that we have all of our prep work done we're

4:06ready to do the actual problem and so step four pick the best conversion

4:11fraction multiply and solve okay so for this first example I'm just going to set

4:17everything up so we have our 16 centimeters over one this is our actual

4:27number now all written as a fraction and so step

4:30one or option one is that we just multiply it with this guy this is the

4:34first conversion fraction that we made so let's just set that up and then we

4:40have another or situation because we could multiply it with this guy so let's

4:45set that guy up too so it's our same number or same number that's getting

4:49converted 16 centimeters over 1 and now we have this second fraction so one

4:55meter over 100 centimeters all right so one of these is going to be correct and

5:00one of these is going to be wrong so now let's just do the math and solve so if

5:06we multiply across the top on the numerator here we're going to get 16

5:10times 100 and so that's going to be 1600 and then remember we have to multiply

5:18our numerator so this is not going to cancel out we have two centimeters on

5:24top so that means that our answer for this will be centimeters squared and

5:28then our ones are going to multiply that's just going to be one and then our

5:34meter didn't cancel out or do anything so that's going to be still here so

5:38option number one we got 1600 centimeters squared over one meter now

5:43this is an ugly gross answer we don't want this so this was the wrong choice

5:48so now let's see what the choice was with the correct conversion fraction so

5:55over here we have and this is the most important part our cancellation this

6:03centimeters is on top and this one's on bottom so we can cancel them out and so

6:09now we multiply it's going to be 16 times 1 so just going to be 16 and our

6:15unit is going to be meters and then on the bottom it's just going to be 1 times

6:21100 so that's just going to be a hundred and there is no unit on the bottom

6:27because centimeter got cancelled out so now we have 16m over a hundred and just

6:33to simplify put it into a decimal or calculator we get 0.16 and our unit is

6:41meter and so this is our correct answer and let's assume we're taking a science

6:51class we have to do sig figs here so our original problem had one two sig figs

6:58just one for each non zero and then our final answer this is not a sig fig both

7:05of these are remember that leading zeros are never sig figs so our final answer

7:09has two sig figs so that's correct and so in these problems our conversion

7:16ratios don't really count as sig figs you wouldn't count any sig figs for this

7:21or this because it's considered like a perfect number so one hundred

7:26centimeters and equals one meter that's not a measurement we didn't like go into

7:31lab and say okay we figured that out that's just kind of a perfect thing that

7:35all of science assumes so we don't have to use sig figs from those two numbers

7:39all right now let's do a couple more practice problems all right

7:46so starting with our first problem convert point six eight five milligrams

7:51into grams so just going to do the same four steps and do them really diligently

7:57and we won't get misled into a wrong answer so step one identify your

8:01conversion ratio so in this case we're comparing milligrams and grams and so

8:08the relationship is that a thousand milligrams equals one gram all right and

8:17so now we're going to write our two possible conversion fractions so our

8:21equal sign just literally becomes a fraction and so it doesn't matter what

8:25you start with on top there's only two options since you only have two things

8:29so our two fraction options are a thousand milligrams over one gram or one

8:40gram over a thousand milligrams all right so one of these is going to be the

8:46conversion unit that we need alright so step three draw your given number as a

8:51fraction including units and so I'd pick this example because

8:55even decimals can secretly be fractions so if you have a decimal just use it as

9:01normal and put point six eight five and milligrams they're all going to be on

9:07the numerator and then you can just throw a 1 under it and that's still

9:10completely fine and so just be really careful make sure your units are still

9:16in the numerator and so now step 4 pick the best conversion fraction

9:21multiply and solve so we're going to set up our original problem number and now

9:29we have to pick what conversion fraction is going to go right here which one is

9:35going to help us solve and so for that we're going to do a little bit of

9:39thinking ahead and our big goal here is to cancel out milligrams the whole point

9:44of the problem is to get rid of milligrams and put it into grams and so

9:49we can see if we put this guy in there milligrams is going to be on the

9:53numerator and that means that you're going to end up with something

9:56milligrams squared and then our grams is going to be on the denominator and

10:00that's not right so what we don't want is to use that one and we do want to use

10:05this guy because we can see right here this milligrams on the bottom is going

10:10to cancel out with the milligrams that we have on top from our number so this

10:14is the one that's going to help us out so we can fill this in one gram over a

10:19thousand MiG's all right and so now let's do some calculator math I don't

10:27feel like solving this right now so we plug that in and we get point zero zero

10:35zero six eight five and then our unit is grams this cancels out and this is our

10:45number and so now let's again assume we're doing it in a science class not a

10:50math class we're going to then have to do sig figs and so our original problem

10:54this doesn't count the leading zero one two three sig figs so we want our final

11:00answer to have three sig figs so none of these leading zeros count one two three

11:06so this ended up in three so this is correct and remember that in

11:12a conversion none of these are going to count for sig figs we just ignore them

11:17the only one that was given to us only one that's a measurement is this first

11:21point 685 okay cool and now let's do our last example convert an eighth of a

11:28liter in to milliliters all right and so step one identify your conversion ratio

11:33once again we're just dealing with two different units liter and milliliters so

11:38one liter equals a thousand milliliters so our two conversion ratios and they're

11:47two possible fractions are one liter over a thousand mils or a thousand mils

11:57over one liter and so now we're going to draw our given number as a fraction

12:02including units and so once again I gave you a different type of number to force

12:06you to think about where your units go and what happens when you convert a

12:10number into a fraction and so this says convert in eighth of a liter so if we

12:16just draw that out it's going to be 1/8 and the way that you see unit's written

12:23next to fractions is usually like this they're right in the middle so 1/8 of a

12:27liter and this is pretty typical but it's really important to know what that

12:31actually means because when we have to assign that unit to a part of our

12:35fraction we have two options right we could do this we could do one liter over

12:418 or we could do this one over 8 liters and one is correct and one is incorrect

12:48and so the big thing to really know is that unless stated otherwise your unit

12:55is on the numerator so this is the correct one we were not told here that

13:00this was the denominator it just was in kind of neutral it's kind of hanging off

13:04to the side but it actually means this not this so if we meant that it was 1

13:11over 8 liters which is completely possible that could be in a science

13:15problem or a math problem we would just have to be told that it would have meant

13:19that in our original problem that would have been shown

13:22okay so now we have our step three done and so now we're going to pick our best

13:27conversion fraction multiply and solve so one liters over eight and I just use

13:35the parentheses because I think that they kind of make it easy to see you

13:39don't need to be using them and so we have our two options and so now thinking

13:44ahead to which one is going to cancel out so we want our leaders down here

13:49because that is the only way that they're going to cancel out right so our

13:53most important thing is to say which conversion fraction allows us to get the

13:58leaders in the denominator because that's the way we're going to get rid of

14:02it and make room for the milliliters and so now if we go we look at our two

14:07different conversion fractions the only one that has leaders in the denominator

14:11is this one which means this is the one we have to plug in this is the one

14:15that's going to allow the correct cancelling and the right answer to

14:19appear all right so now let's do our multiplication and do some canceling out

14:26so if we cancel these guys out and we know we're going to end up in mill and

14:32so basically we have a thousand over eight and that turns into 125 and so

14:40that's our answer so just talk about sig figs a little bit in this problem so we

14:46had it written up here as an eighth it was just words not numbers and so the

14:52way that I run my classes is when you see that it means that you don't

14:57consider sig figs that you just consider it to be an eighth is like a perfect

15:01number kind of like our conversion ratios we wouldn't consider one liter or

15:05a thousand mils to either them have sig figs but I think every teacher kind of

15:11does it on their own so if you're in taking a test and you don't remember

15:14what your teacher said and you see some kind of word written out you can

15:19definitely ask them that's fair game there's not one standard way that

15:24everyone should be doing that that's all I have for you today I hope you enjoyed

15:28this longer very detailed explanation of how to convert units again I really

15:35think that if you store with this topic this is the way that

15:38makes you think about every step that doesn't allow you to have a pitfall

15:42where you take a wrong turn this is really the way that forces you to do it

15:47correctly even though it takes longer but hey when you rather take longer and

15:51get the answer right then do a shortcut you don't understand and not know if you

15:55got it right this is the teacher nagging side of me coming out I can't control

16:00happens everybody starts teaching chemistry I think anyway that's all I

16:04have for you today I hope you enjoy this video and have a good day