All right, we're going to start um sections 1.4 and then I'm going to throw in some section 1.7 here because it's relevant to your homework for the week. So, we're going to start with talking about measurement. Measurement is um going to be really important, especially if you're taking the lab component of the class. But a lot of the things that we're talking about in chemistry, even in lecture, are measurements. A measurement is going to be composed of two things, a number and a unit. A unit is really important. The number means nothing without the unit. So if you were to give an example of, hey, um, this patient needs 325 of aspirin. You would have to say, okay, of what? Millig, pounds, like you could really hurt somebody if you give them 325 lbs of aspirin, right? So, you have to be um more descriptive when you're talking about uh things in chemistry. In chemistry though, for I'll just go ahead and tell you that when you're talking about measurements, when we start to do our math, the best way to think about it is going to be three pieces. You're going to have a number, then you're going to put the unit, and then you're going to put the substance. What is it? So number plus unit plus substance and that is going to give you a complete description of a thing you're talking about. So 325 mg of aspirin, right? um just to make sure that you're very clear with your work and that other people that are reading your work later or um you're communicating things to other people. Cuz a lot of part of science is communication that you're clear in communicating to yourself in your notes and to other people exactly what you're talking about. Cuz if you just say 325 milligrams of of what? Right? So you need to make sure that you're conveying that. So, if you're the type of person that's like, "Oh, I really just like to do my math and write in a number and be done with it." Go ahead and start getting yourself comfortable with writing a number, writing a unit, and writing a description of the substance or the thing that you're talking about as your full answer or your full like whatever you're writing for that moment. Sometimes I'll drop the substance because I'm trying to go fast like on a test. If I know I'm not really changing substances in my work, I'll drop the substance out because I know the question is talking only about aspirin, for example. I'll just use a number in a unit. But if you are doing a complicated problem, the more complicated you think the problem is, the more stuff you need to write out and organize. So, go ahead and get used to thinking about three things we want to write down with a measurement or a number in a math example or anything like that. The metric system is what we're going to use in this class. Um, not the English system necessarily. So, every type of measurement has a base unit in the metric system. Length, the base unit is a meter. The symbol is lowerase m. It's got to be a lowercase m. Mass, the base unit is gram, lowerase g. Volume is liter uppercase L. Um, you can technically use lowercase L, but lowercase L often looks like an I to some people. So, we use uppercase L's to be very clear. We're talking about a liter. And time, the base unit is second, which is S, not S E C, just S. Metric system is also great because it has prefixes that go in front of those base units and then change by a power of 10. And so if you just take your base unit and you multiply or divide it by 10 a certain number of times, you get other units. These are something that you need to memorize. So this is on your memorization list. This table 1.2 there's other stuff for memorizing like um a few say not memorization memorize. I need to memorize this list here. It's on your memorization list, which is a link in D2L and sent out to you in that welcome email. But, uh, you need to know basically, you want to know what the prefixes. So, we want to do this. I would probably put this and the symbol on the same side of the flash card just so you're familiar with the word, but also the symbol because you may see both in the question. And then how you how do you know how to say it? Right? So the prefix and the symbol and then on the other side of your flash card you should put the scientific notation not the numerical value because the numerical value while helpful for some of them is kind of hard for others and instead of memorizing them where some of them I use numerical and some of them I use scientific it's kind of easier just to me memorize them all in one way. So know that a giga is 10 the 9, a mega is 10 6, a micro is 10 - 6, a millie is 10 -3. So on one side of my flash card, I have the prefix, the actual word to make sure I know how to say it. And then the symbol, the symbol here, micro, is sometimes often written as MC, especially in uh healthcare where it's hard to read people's handwriting. So, it's either the Greek letter mu, which is kind of like an M uh like a U with a little tail coming up. So, draw it as like a U first and then put a tail on the end. Um, or abbreviate it again as MC. So you could like mcg would be microgram. We put these prefixes in front of whatever base unit we're using. So here are your base units. Meters, g, liter, seconds, and I mean anything could technically be a base unit. Like you could say um mega dogs and that would be 10 the 6 dogs. It doesn't matter what your base unit is, dollars, doesn't matter. You put this prefix in front of it and it gives it a new meaning. Some prefixes mean a small amount of something like desi cinti millie micro nano and the other prefixes mean a large amount of something kilo mega giga. So know which ones are small and which ones are large. Maybe you do that as a color coding in your flash cards. Smaller get a certain color, big ones get a different color. Um and then all you have to memorize is what number after the power of 10, what exponent it is. So you can memorize a kilo is a th00and like some people know that like a kilo is a th00and um but also 10 to the 3 is the same thing as a th00and so however you want to memorize it pick something that works for you and stick with that um for centi you may not have memorized 01 maybe you know 100 centi is a thing well 100 is just 10 the positive2 so I'll talk a little bit about how we can kind of switch that up um if If we kind of change the sign on the power of 10, then we kind of think of that number as being in front of the prefix instead of opposite of the prefix. If that all confused you, you have no idea what I'm talking about, just set up your flash cards with these on one side and these on the other. And then once you have that memorized, I will show you how to use them uh to do calculations. Um, yes, you can bounce your decimals around between these, but you have to know that not all of them, like this is not a jump from 1 to 0. So, you got to be careful about memorizing like this is these are not all the same jumps. Um, but you can move decimals around if you want to. However, if we once we get up into like the really big and really small, moving your decimals around is not quite as effective as actually having um a conver a memorized prefix and using as a conversion factor, which I'll show you at the end of this video. So, measuring length, um the base unit for length is a meter. So, for example, a kilometer is 1,000 m. You can also think about a kilometer because kilo means 10 3. So if I have my flash card and I memorize kilo means 10 3, I can just put a base unit on either side of that equality and then put a one in the front of the prefix side. So to turn this definition into into like an equality um I can write the base unit or the prefix first. So for millie my prefix is m little mie means 10^ the -3. That's what I memorized. Then I can put in a base unit behind each of them. Now the base units got to be the same on both sides. This one is meters. So I put a meter on this side. I put a meter on this side because what I'm saying is that millie equals millie. So millimeter equals millimeter, right? Because 103 and millie mean the same thing. Put a one in front of your prefix side. Now you've got a nice little equality that we can use later. And then lastly, we have centi. Centi means 10 to the -2. Put the base unit on both sides. M. M. Now I have 1 cm equals 1 cm because centi and negative -2 10 the negative2 are the same thing. Now what did I mean about that? Um earlier I was talking about how we can move the decimal around or I can say 10 to the pos2 cm is a meter and what is 10 the positive2 100. So maybe you have memorized a 100 centsis as a thing. That's fine. Whatever you have memorized, work with it. Um or if you're like, hey, I'm new to this. Just say centi means 10 -2 and just memorize the you need to memorize some sort of equality. Um and we'll put whatever base unit on the end that we want. You can move the exponent to live on the same side as the prefix. If you move the exponent though, you've got to change the sign. If you change the side of the equality for the exponent, we change the sign of the equality. So think about it like this. Centi is small, right? Smaller than a meter. So a lot a big number of little things go in a bigger thing or in one small thing there is a small fraction of bigger things. So make sure that you don't do this. 10^ the -2 cm equals a meter because that is not true. That's saying that a small number of little things makes a bigger thing and that and that can't be true. So just be careful if you change the side of the exponent. You have to change the sign of the exponent. And you may already have these memorized in a certain way. Whatever works for you that you continuing to get right on problems, then keep doing that thing. But if you feel like you're struggling with it, you can pick this method up. For mass, we're going to measure mass and weight. We're going to kind of use them together. Technically, mass is the just amount of matter that you have, and weight is that with gravity. But because we're kind of all on the same planet right now, uh we are our mass and weight is, you know, we really are using weight when we weigh things. Um because gravity is pulling us down. Um but because it's all universal on the planet, like the gravity is the same constant kind of wherever your weight is the same. So that we can kind of equate mass and weight together. Um, however, if you were to go to the moon, for example, your weight would be a lot less, but your mass would stay the same. So, weight is just matter with gravity and mass is just amount of matter. So, we use mass as grams as the basic unit. And so, here are some more of those conversions. Kilo means 10^ the 3. 10 3 is also a th00and, however you want to memorize it. Put a base unit after it. G. G. put a one in front of the prefix side. So now we have what we can memorize turned into these equalities. Millie is 10^ the -3. Put gram on both sides. Now what if you want to change that around? You could say 10 the pos3 mill is equal to a gram. What is 10 the positive 3? 1,000. Maybe you want to memorize a th00and millies as a thing. That's fine. Whatever works for you. And then lastly, volume. There are two types of volume that we can um really talk about. The first is a liter based volume. So a kind of single unit based volume like ounces, liters, gallons. These are all liter based volumes. So think about kilo is 10 3 or 1,000. Put a liter on both sides. Put a one in front. There's how you use what you memorized. Millie 10 -3 putting a liter on both sides. So we have that and the other type of volume is a lengthbased volume. So these are our liter based volumes. So that'll be lers, gallons, ounces, um etc. Any sort of liter based or single unit based volume. And then you have length cubed based volumes. This would be like centime cubed, me cubed, inches cubed, miles cubed, whatever length you're talking about cubed. That's a different it's a it's still a volume because it's still measuring shape space, right? that it's different in kind of how we're measuring it maybe or the unit in which we're giving that. Um the way to go between those two types of volumes is here. So you need to memorize this. 1 milll is equal to 1 cm. And a cubic cm is also known as a cc. Cc standing for cubic cm. And this is really important if you're going to go into the healthc care field because you'll see cc all over the place. uh cc is just a milliliter or a cubic cm. Um having that memorized though is going to really help you because you may have a problem where you start with a liter based volume like microl, millilit, kiler and you need to go to like me cubed or something. So this is a great in between and it's good to memorize because it's just one one. There are some other units of measurements that we um will use especially between the English and the metric system. Um so stuff that you probably know already but want to memorize. Uh a foot is equal to 12 in. Um those are just within English. Um but then 2.54 cm is equal to 1 in. Um it says exactly. We'll talk about significant figures and why it says exact later, but uh some numbers are exactly that and some are measured where it's kind of roughly. If it's within the same unit, like they're both English, then it's exactly like the definition of a foot is 12 in. If it's between two of them, you'll notice these numbers have more fractions and more numbers like that that actually are measured. Um so we will be concerned about the number of digits in that measurement. Um you'll also want to memorize this one. I think on your memorization sheet I have 2.20 instead of 2.005. If you can memorize an extra five, it will help you be a little more um accurate in your answers. Um but you don't have to really worry about anything else on this. Um anything would be given to you on an exam. These three would not really be given on an exam. So I would memorize them. You also want to memorize all your time stuff like a day is 24 hours. There's like all these kind of things that you kind of know, but just make sure you know those different measurement um conversions or equalities. This these are these are very commonly used this one especially in healthcare when you're doing dosage stuff. So, um how do we use these things? So, we're going to talk a lot more about this a little bit later in unit one, but I want to go ahead and just give you like a breakdown because there are some homework questions this week that you'll want to do this with. Basically, if we decide that we want to talk about something in a different unit than what we measured. So, for example, if we measured something in you measured your patient's weight in pounds, but you look at the dosage of the medication and it's per kilogram, you need to convert pounds to kilograms or vice versa. um you'll take the original quantity and you'll multiply it by some conversion factor. The conversion factor is an equality. So two things that are equal to each other written as a fraction. And when we multiply something by a fraction, then we can cancel out units we don't want. So for example, um 2xy over y, the y's will cancel out, right? So we can cancel out units if we kind of put them into fractions with each other. Multiplying two fractions together, you know, you just get one big fraction there. So we can cancel units out that we don't want. Um, and I'll I'll show you more about this a little bit later, but you will do a lot of work taking conversion factors written as equalities using them as fractions to convert between unit um you want and a unit you don't want or vice versa. A unit you don't want turn into a unit that you do want. The thing about the conversion factor method that we're going to be using is that the amount that we start with and the amount we end with are actually the same amount. Like if I weigh my patient in pounds and then turn that number into kilograms, did I change the weight of the patient? No. I'm just telling you in a different thing. So if two things are equal to each other, for example, if three equals 3 and I put three on top of three, that just equals 1. So if I take 2.205 lb equals 1 kilogram and I use it either way, I can put however flip to that fraction I want. If I put those two things that are equal to each other on top of each other, the actual value of a change in the measurement is like multiplying by one. So yes, we're changing the number, but we're not changing the actual measurement. If I weigh myself in pounds and then convert it to kilograms, I did not change the how much I weigh. So it's really key. These two things are really important. The two things you're putting on top of each other in the fractions must be equal to each other. Two things on top of each other must be equal. They must be equal to each other. If they're not equal to each other, you cannot put them on top of each other and then have this thing where your measurement is actually the same as your answer in how much it really is. Just represent it in a different way. If that doesn't make sense to you, come talk to me and I can try to reward it a million ways and help you understand that concept. So, if we had um if I weighed someone and they were 130 lbs, we're going to multiply it by conversion factor to get kilograms because maybe the medication I'm looking at tells me how much to give per kilogram. So, I take my pounds, I'm going to convert it to kilogram. Our goal is to figure out how do I get rid of the pounds? If I put that kilogram to pound conversion and I use it this version of the fraction. So remember there's two kind of versions of this fraction. 1 kilogram is equal to 2.205 lb. I can write it as 1 kg over 2.205 lb or I can write it as 2.205 pound over 1 kg. So, I think about which one do I need to insert here to get rid of pounds and to get kilograms. Well, if I have a number on the top of a fraction or a unit on the top of a fraction and a unit on the bottom of the fraction, they will cancel out. So, if I want pounds to go away, I got to put pounds on the bottom of the fraction. Remember, this is really just like over one. So, this is just one long fraction here. Actually, that's how I do it. I just kind of separate them. uh where it says times, I just put a little line there instead of the times. I want you to be very certain of the top and the bottom of not only the first number that you have, but also all the fractions later. So multiplying two fractions together is kind of just like putting them all into one big fraction. Everything on the top, everything on the bottom, and the relationship between everybody on the top um with each other is multiplied. And the relationship between everybody on the bottom with each other is multiplied. Overall, the relationship of the top to the bottom is the bottom is divided, right? But we can think about it as being the one big fraction like that. So the pounds are cancelling. So this would give me the same weight. The person's weight hasn't changed, but the way in which I state their weight is different. 59 kg is equivalent to 130 lbs because two things on top of each other that are equal to each other really kind of just mean one. I know numerically it doesn't, but the the actual meaning of the value is the same. 130 lb is equivalent to 59 kg. I hope that makes sense. If not, definitely see me after class. Talk to the LA when we're doing work. Um we can make sure to get that concept good for you. So, here's an example. I want you to pause the video and see if you can think about how to put this together. How would you take 325 milligrams and turn it into grams without just moving the decimal around? Think about what is a millie, write an equality, and then see how you could use that fraction. So, pause it real quick and see if you can try. If you get stuck, you can always come back. So, if you got a little stuck, I'm going to move on to step two, which is just writing your conversion out. So if I know I need to go if I see millie I can just write this conversion. I know a gram is 1,00 millig or maybe you did um a millie is equal to 10 -3 g. Maybe you have it like this. Doesn't matter. If we have an equality we can use it as a fraction. One thing on top of the other. So either side of the equal sign goes on top that equal sign becomes like the fraction horizontal line. So, which one do we need to use if we want to start with millig and get rid of millig? So, pause and see if you can figure it out now. Okay, so hopefully you're able to do some work, but here's the kind of final answer. So, if we have 325 millig, we're going to multiply that by one over a gram over milligram. Maybe you have um 10 -3 g and 1 millig. Maybe that's what the fraction you have. Either way, it's going to give you the same answer. And then you just do that math. Whatever's on the top gets multiplied. Whatever numbers in the bottom gets divided. So 325 divided by 100 cuz it's in the bottom of the fraction gives you.325. We'll talk about significant figures later, but that's kind of the gist. All right, we'll do a lot more practice with this, but it'll be really important to learn this topic. So go back and rewatch this video and do some practice on this to make sure you understand how do I take inequality and then use it to convert between different units.