Wow, we've been talking about the number a lot, haven't we. And we're forgetting to talk about the unit. I never want you to forget about the unit, so let's go back to that. Whenever you have a measurement remember you must have a number and a unit. Without an associated unit, the number is, of the measurement is meaningless. I'm going to say that again because students leave off the unit so much that I think it's worth saying twice. Without an associated unit, a measurement is meaningless. Now in science, we tend to use the metric system as units for measurement. And the standard units of measurement in the metric system are, the gram for mass, abbreviated has lowercase g. The meter for length, abbreviated as lower case m, the liter for volume, abbreviated as capital L. I don't know why they decided to use capital, capital for that, but they did. And time we use seconds, abbreviated as just a lower case s, and for temperature we can use either celsius, which is degree c. Or Kelvin, which is just capital K. So those are the standard units. You might live in a country that uses other units, for example, I live in the United States and for Mass we often use Pounds or Ounces. In science, we pretty much always measure things in grams, meters, and liters. We very rarely use, measurements like a cup of liquid or a tablespoon of liquid. So it just depends which country you're in, which units you might routinely use around your house, but in science, we've agreed internationally as a group of scientists, that we're all going to use the same types of unit. Now, a gram is not a very large quantity I suppose, well I guess it could be a large quantity if you're talking about a diamond that weighs a gram. But, we can modify these units using prefixes for the metric system, to show numbers that are very large or very small. Here's some that I think you should know. The prefix mega, which has the symbol capital M, is the equivalent of 10 to the 6th. So if I had a megameter, that would be 10 to the 6th meters. If I had a megagram, that would be 10 to the 6th grams. Your probably more familiar with the kilogram. That's used, that's used to weigh people's body mass for example. And that's the gram times 1000. I don't use deci very much honestly, but centi get's used a lot in measuring length. The centimeter is smaller than the meter. In this case it's 1 100th of a meter. So there's 100 centimeters in a meter. So it's a meter times 10 to the minus 2 if we're using scientific notation. Other common prefixes that get used to show very small quantities are milli, which is 1 out of a1000. Micro, which is the unit times 10 to the minus 6, and nano, which is the unit times 10 to the minus 9. Sometimes in chemistry we go even smaller that that. We might use pico, pico, which is a lowercase p, and that's the base times 10 to the minus 12. It would be really tedious to write that number out with all of the zeroes. So I'm not going to do that, that's part of the reason we use scientific notation. If you're from a country that doesn't routinely use the metric system, you might be used to dealing with measurements like yards and miles. Perhaps you use pounds or quarts. So I want you to think about, which of these is larger? What's longer, a yard or a meter? Which one's longer? A meter is longer than a yard. How bout a mile or a kilometer? Which one of those two measurements is longer? So again I've got two measurements. They're each have a number of one. But the unit is much different. So which one's longer, the mile or the kilometer? Hopefully you realize that the mile is longer than the kilometer, but if you live somewhere that doesn't use miles, you might have no idea, and that's okay. These are crazy units we use in the United States. An inch is larger than a centimeter, it's about 2.54 centimeters. A kilogram is heavier than a pound. Sometimes people in the United States have trouble with that because many people in the United States seem to know that a mile is longer than a kilometer and then when they get to kilograms and pounds, they get confused. How about this one. Hopefully everyone can do this one. Which is larger? One milligram or one microgram? Those are both pretty light weights but hopefully you said one milligram is larger. Let's talk about some volumes. Which is larger a quart or a liter? A liter is larger. How about a liter or a gallon? I buy my milk by the gallon. A gallon is larger. Which one of these is larger, a gallon or a thousand cubic centimeters? This brings up something that I think is really important to know. In the metric system, the volume of a milliliter, just write that down, one milliliter was defined as the volume of this bounded by one centimeter by one centimeter, by one centimeter. In other words if the length, width and height of something is all one centimeter that's a milliliter. So I could draw a little cube, right, and if all the sides are one centimeter, the volume inside that cube is one milliliter. In other words, a milliliter is one cubic centimeter. Sometimes that's written as one cc. They often talk about that way in medicine. So I think that's really important to know. So what I'm saying down here at the bottom when I asked you about the gallon or a thousand cubic centimeters. Well that's asking you about a gallon or a thousand milliliters. Which is the same as asking you about one liter. So a gallon is still larger. What I was just doing there, although I was doing it in my head, was I was using conversion factors. Conversion factors allow you to switch easily between units, and they can easily be looked up. You can look them up on the internet, or you can look them up in, any chemistry book that you have, probably has them in the, in inside front or back cover. Here's an example of a conversion factor that I've had to use a lot because I used to work in industry and I was in the United States where we measured things in gallons and pounds and we were forming a joint venture with a company in Germany, who of course measured everything in kilograms and liters. So all the time I was converting between kilograms and meters and I memorized that 1 kilogram equals 2.2046 pounds. It's easy to convert using dimensional analysis. For example if I asked you what is the mass in kilograms of a 65 pound sack of flour? How would we do that calculation? Well with dimensional analysis what we would do is, we would start with what we have, 65 pounds, and then I would use a conversion factor. I'm going to write the conversion factor as a fraction. I want the fraction to have the unit that I don't want on the bottom. So I'm going to put pounds on the bottom. 2.2046 pounds. And the unit I do want on the top. 1 kilogram. So to do this calculation, I'm going to take 65 and divide by 2.2046. And that's going to give me 29 kilograms. I would need to use a calculator for that, but I already did. So, I figured it out. The last thing I want to talk about, is why do we use scientific notation? Now one of the reasons I showed you already that we use scientific notation, is because it's a very easy way to indicate the correct number of significant figures, without confusion about zeroes. Another reason we use scientific notation is to not have to write so many zeroes, when we are writing down very, very large or very, very small numbers. I'm going to give you some examples of very, very small things. What's the diameter of a gold atom? Do you have any idea? Turns out a gold atom is 2.7 angstrom in diameter. 2.7 angstroms. And an angstrom is 10 to the minus 10 meters. So if I wanted to write the diameter of a gold atom in meters, I would write 2.7 times 10 to the minus 10 meters. I wouldn't want to write all those zeros down. I guess I could. Let's do that. How many zeros would I have to write after the decimal point, I'd have to write nine. One, two, three, four, five, six, seven, eight, nine, one, two, three, four, five, six, seven, eight, two, seven. Did I do that right? I think I did. That's tedious. That's a great reason to use scientific notation. Another thing I hope is a very small number is the concentration of arsenic in my apple juice. What do you think the concentration arsenic in my apple juice is? Well the, the Environmental Protection Agency in the United States says it has to be less than three parts per billion. Well how much is three parts per billion? Three parts per billion is 3 times 10 to the minus 7 percent. That's not very much Arsenic. Hopefully it's less than that. So I'm hoping that my concentration is less than three times 10 to the minus seven percent. How about some very very large numbers? Atoms are so tiny you'll see quickly that if we're looking at, even, a relatively small amount of molecules or atoms, the number of molecules and atoms can be very large. In other words, if I had a cup of water, how many water molecules would that be? Turns out that would be 8.36, times 10 to the 24, molecules of water in one cup of water. This little coffee cup. It's a lot, that's a large number, I would never want to write that number without scientific notation because, I'd have to write a lot of zeroes, 22 zeroes, wouldn't I? How about the US national debt. Well that goes up and down. So that budget deficit fluctuates, but last time I looked it was 642 billion dollars. [SOUND] Which is a huge number and I can write that as 6.42 times 10 to the eleventh power. Other numbers that are very larger, things like populations of countries. If we looked at the entire world, the UN projects the population of the world would be 8.9 billions people by the year 2050 that's there middle estimate. It's not their conservative estimate which is lower and it's not their oh no, over population estimate, all though 8.9 billion is probably over population. But 8.9 billion people is 8.9 [SOUND] times 10 to the 9th people. If you write all those zeroes down there, you'll see that that's a very large number of zeroes. I've enjoyed this review of measurements and significant figures. Remember, measurements contain both numbers and units. Use the correct number of significant figures to show the precision of the number, and be careful to consider how any mathematical operations are effecting the number of significant figures. It's extremely important to keep track of the units. And I suggest writing the units down every single time. If your not in the habit of doing that I hope you can change that habit. Finally, unit conversion factors are just ratios. And those ratios can be written as fractions, with either quantity in the numerator. You can use those fractions to do dimensional analysis and convert units. We're going to be talking about many measurements in this class, and we're going to be performing calculations and unit conversions routinely. So please take advantage of the practice exercises this week.