Okay, today we need to talk about measurements and how quantitative observations work. This is literally going to be what the entire rest of the chapter is going to be about. Okay, so the idea is that anytime you have a measurement, there is always going to be a number component and a unit. In chemistry, both of these are really, really important.
You will find that most chemists, including myself, are going to be really, really nitpicky about you putting units on everything and labeling everything correctly. Okay, so... Both of these are going to be important. So if we had like 43.7 kilograms, okay, the number part is going to matter. How many decimals it has is going to matter.
How accurately you measure things is going to matter a lot. The unit, the label of it, is also going to be important. We are actually going to talk about the units first because it's the easier of the two and it doesn't really matter which one we do first.
So basically units are like a label. They're just describing what we're talking about. So I know I'm just a voice in a video looking at things but you guys are gonna see me in class so it's good enough.
You know if I stood in front of you and told you that I am 70 you'd probably call me a liar. Most people don't say that I don't even look older than like you know 30 even though I'm older than that. But since I didn't put any units on it, you guys assumed I was talking about age.
But if I told you I am 70 inches tall, that's actually correct. Or if I told you I weighed 70 kilograms, it's pretty close. Okay, so the labels...
matter. If you just have the number, it's not going to mean as much if you don't have the unit, and if you just have the unit, that's not going to be as, it's not going to mean as much as if you have the number also. You absolutely need to have both, and you will find that as far as grading for quizzes and exams, I'm kind of nitpicky about that.
Okay, for units, there is the, the, what's it called, the empirical system. I think this is what it's called. For some reason I always forget the name of this.
The Empirical System, which basically you could visualize as like the British units. The British people came up with this. These are things like... pounds, inches, feet, degrees Fahrenheit, etc.
Okay, a lot of times they are based on like cutting things in half or cutting things into a third and they tend to be really a pain in the butt honestly, but the problem is we live in America and we still use these things. So if I told you, you know, Like I'm 5 foot 10. Like you know what I mean. Those are normal things.
If you move to any other country in the world, they don't do this. Okay. The one that we are going to use more often than not is the metric system. Okay. These are things like grams, centimeters, degrees Celsius, liters, stuff like that.
These are just random examples. These are the default scientific answer. These are These are also the default answer for most of the rest of the world.
If you went to France and asked someone how much they weighed, they would probably tell you in kilograms. If you asked how what temperature it was, they'll probably tell you in degrees Celsius. If you ask how big something is, the volume of it, they'll probably tell you in liters.
So the idea though is that... One of the hard parts for us is that this is the default answer. The metric system is the right answer.
We are used to doing things like this. So when I tell you it's 75 degrees outside, you interpret it in Fahrenheit. If it's 75 degrees in Celsius, that is a very, very different answer.
So when we talk about unit conversions, which I'm going to... Right out here. What we're talking about is converting from one set of units to another. Okay, the way I visualize it is like basic algebra. So if you had two things that were equal, so this is the algebra explanation.
If you had two things that were equal, a equals b, and you had a divided by b, that would be equal to 1, because these two things are equal. Similarly, b divided by a is also equal to 1. Anytime you multiply anything times 1, it doesn't change. change.
So we can use the same logic with unit conversions. So for example, one foot is equal to 12 inches. Okay, so if I say that I've got, you know, 2.13 feet and I want to know how many inches is that.
Okay, I'm converting from feet to inches. Essentially what we're gonna do is we're gonna start with what we know. I'm fully aware that you guys probably learned this in like junior high.
I have kids, like my children know how to do this. But I also want to make sure we all know how to do it the same way. Essentially what we do is we take one of these two sides of our unit conversion, like A equals B, one foot equals 12 inches, and we put one side on top and one side on the bottom and we multiply it by our original thing because that's the same thing as multiplying by one. I am going to set this up so that the units cancel out. I need feet to cancel out, so this side of this equal sign has to go on the bottom, and this side has to go on top.
Feet will cancel out and we'll have inches which means we converted from feet to inches which is encouraging. Our units cancel everything out. I am not asking you to memorize that when you're converting from feet to inches you multiply by 12. What I'm asking you to do is realize that if you have this unit conversion you're gonna plug it in here that one side goes on bottom and one side goes on top.
The side that goes on bottom is the side that's going to cancel out the units. So we have feet on top, we need feet on bottom to cancel it out. Typing this in your calculator This is going to work. Basically anything that's on top you multiply, anything that's on the bottom you divide.
So 2.13 times 12 it equals, and I got 25.56 I'm gonna round it to 25.6. We haven't learned sig figs yet, but we will very very soon. Okay, and this should hopefully make sense if you think through the answer. If 12 inches is a foot, 2 feet would be 24 inches, and this is a little more than 2, so this should be a little more than 24. So the answer makes sense.
It should be super, super consistent here. Okay, let's try a couple more here just to make sure we got this. Okay, let's say we have...
17.3 grams, and we want to know how many pounds is that. So in this case we're switching from metric to empirical. Okay, I do not need you to know the unit conversion off the top of your head. of your head I will provide the unit conversions. Okay, it turns out that one pound is equal to 453.6 grams.
Okay, so we set up what we know which is 17.3 grams. And this is our unit conversion, so it's got to shove in here somehow. One side's got to be on top and one side's got to be on bottom, but we don't know which is which yet. So we have grams here, we're going to shove this side, which is grams, on the bottom.
And then one pound will go on top. So our grams cancel out and we're left with pounds, which is the unit we were solving for, so we're good. Okay, this time we're going to divide because we have this on top and this is now on bottom. So 17.3 divided by 453.6 because that's the conversion factor and we get an answer of 0.038.
One. Okay, and we put a unit on it because the units are important. All right, let's try one more that's a little more cumbersome.
So let's say we have 55 miles per hour. I know if you see it on your cards written as MPH, as far as units, it's miles that are happening every hour. So hours is on the bottom.
And we want to know how many meters per second is that? Okay, there is probably a direct conversion, but I have no idea what it is. I can convert from miles to meters, and I can convert from hours to seconds, but I still don't know it in one conversion each.
So, I do know that one mile is 5,280 feet. I do know that one foot is 12 inches. I do know that one inch equals 2.54 centimeters, and I do know that one meter is 100 centimeters.
So it may take me four steps, but I can get from miles to meters. I also know that one hour is 60 minutes, and I know that one minute is 60 seconds. So I can convert from hours to seconds in a couple steps.
So this is gonna take a lot of steps, but it's the same process. You just pile them all together and cancel out the units as you go. So 55 miles per hour.
I have all these things to work with. I need miles to disappear. I need it to cancel out.
So I'm going to put miles on the bottom. And this first one is the only one that has that. So one mile goes on bottom, so the other side has to go on top, which is 5,280 feet. Miles cancels out. Now we have feet.
We're solving for meters, but we're not done yet. We need feet to go away. So one foot goes on the bottom, the 12 inches will go on top.
So feet cancels out and you're left with inches. Now we need inches to go away, so one inch goes on the bottom, 2.54 centimeters goes on top. Okay, now we need centimeters to cancel out. 100 centimeters will go on the bottom, and one meter will go on the top.
Centimeters cancels out. We have meters on top. In the end, we are looking for meters on top, so we are going to stop here. That's fine. We've cancelled everything out.
You'll notice I did not tell you when to multiply or divide. I just made the units cancelled out. I had miles on top, so I made miles go away by putting it on the bottom. Feet cancels out with feet. Inches cancels out with inches.
Centimeters cancels out with centimeters. We end up with meters on top. We still have to convert hours to seconds though. Now we have hours on on the bottom so we need one hour on top and 60 minutes on the bottom. And we need meters per second, so 1 minute is going to go on top, and 60 seconds is going to go on the bottom.
And in the end, everything is cancelled out except for meters and seconds. And that's the units we were looking for, so we must have done it right. Now, as far as typing this all in, this is going to be kind of a pain. Basically, anything that's on top you multiply, and anything that's on bottom you divide. I'm going to recommend instead of hitting parentheses a bunch, I'm just going to recommend you hit equals a lot.
So, 55. times 5280, because it's on top, then I hit equals. I don't care what the number is, but now I'm gonna multiply by the 12, because it's on top, hit equals, times 2.54, hit equals. We have some stupidly large number, but we're done multiplying all the top stuff. Now we need to divide each of the individual bottom things. So divided by 100, hit equals, divided by 60, hit equals, divided by 60, hit equals.
And I got... basically 25 in roundup. Okay, so there's three different examples, but...
Even if you do unit conversions a little differently than this, as long as you get the same answer, I agree with how you did it. I will tell you that as the class goes on, as we start getting to weirder unit conversions, like converting from grams to moles and weird stuff like that involving specifically chemistry, I am going to set up all my problems like this. So learning how to set it up like this is going to be critically important. Thank you.