 Greetings and welcome to Math Help for Science courses. In this video, we are going to look at the metric system and discuss that and how that is used for measurements in science. So that is what is primarily used around the world, except the United States in general uses a different set of units, although the scientists within the United States really do use the metric system for scientific work. So let's look a little bit about what the metric system is in the first place, and it is sometimes called the International System of Units, or SI units. You will sometimes see that terminology as SI units is the most commonly used system in the world. It began back in the 1700s and was designed to be a very simple set of units based on powers of 10. So the difference in when you're using English units in that there are 12 inches in a foot and 3 feet in a yard, we know that in the metric system, there are 10 millimeters in a centimeter and 100 centimeters in a meter. Everything is done by powers of 10. And there also are not differences between different types of units. For example, in English system, we have that there are how many ounces there are in a pound. Well, there are 16 ounces in a pound, and there are 12 inches in a foot. In metric system, they're always the same. So there are 1,000 millimeters in a meter, and there are 1,000 milligrams in a kilogram. So they are always exactly the same, regardless of what set of what measurements you are doing. Within the metric system, there are seven base units, depending on the science class you're using. You may use some or all of these. Typically, most classes will use distance, the meter, mass, the kilogram, and time, the second. So those are very commonly used. Others are used less often depending on the class. Temperature units often used in kelvins will sometimes be used. And the amount of matter being the mole would be used in chemistry classes. And electric current, if you're doing electricity, would be the ampere. And the luminous intensity, or the candela, would be the last of these seven units. But everything is based on these seven, and anything else that we use is derived from these. So for example, if you wanted to look at velocity, velocity would just be a distance divided by time, or a meter per second. So why do scientists use the metric system? And we do that because it is very good having everyone using the same set of units. You don't have any confusion with things measured in meters and things measured in feet. We don't have to do any weird conversions to get between one or the other. And as I said, they are based on powers of 10. So we know that there are 1,000 meters in a kilometer, and not the English system, where there are 5,280 feet in a mile. So it's much easier to do conversions, much easier to remember numbers. There are not a whole bunch of conversions to remember. What you really need to know is the table of prefixes. And that tells you what the power of 10 is. You may be familiar with some of these basic ones. Giga, meaning 1 billion. Mega, meaning 1 million. Kilo, meaning 1,000. Centi, meaning 1,100. Millie, meaning 1,1,000. Micro, 1,1 million. And nano, 1,1 billion. So you may have heard of things like nanoseconds or microseconds or milliseconds. And those are tiny fractions of a second. So you use a number of these. We talk about storage. We talk about megabytes or gigabytes. Those are all, again, measuring units here and using the same type of prefixes that are used in the metric system. So let's look at a couple of conversions and see how we can do this here. Let's look at some examples of how we would go about converting these types of things. So just for our first example, we would have the, we have 1 million meters. So we'd write down 1 million meters. And we'd want to convert that into kilometers. So how many meters are there in a kilometer? Well, kilo means 1,000. So 1 kilometer equals 1,000 meters. How do we go about converting that? Well, we can take this and divide it out and write this up in this train track form. And that would then say we'd want to get the units to cancel. So we would say there's 1 kilometer per 1,000 meters. And if we look there, that means that when we look at the cancellation, our units cancel, meters will cancel. And we will take 1 million divided by 1,000. Or that 1 million meters equals 1,000 kilometers. So we've just done the division here and just used the conversion that 1 kilometer equals 1,000 meters. Now we can also convert this 1 million meters using the same method into millimeters. So we have 1,000 meters. Now we have to think how many millimeters are there in 1 meter? Well, 1 meter equals 1,000 millimeters. Now you might think this looks like it's going to give us the same answer we got before, but let's put this together. And we would then have now we want our units to cancel. So it's 1 meter down here and 1,000 millimeters in the top. So when we cancel now, we're still canceling our units correctly, meters are canceling. So we will get an answer in millimeters. And in this case, it's going to be 1 million times 1,000, or this equals 1 billion millimeters. So you're doing the same type of conversion, but you always have to put things together so that their units cancel properly. So in one case, when you're converting meters into kilometers, you are dividing by the 1,000. And when you're converting the meters into millimeters, you are multiplying by the 1,000. So let's do this now for grams instead of meters. So if we have 1 million grams of something, and we want to convert that to kilograms, well, 1 kilogram equals 1,000 grams. So as we draw our conversion here, we would then put our units in here to do the conversion. Again, we want to make sure the units cancel. So we have to put grams down below and kilograms up on top. And that ensures that the grams cancel, and our answer will be simply 1,000 kilograms. And we can do it again if we wanted to convert this to milligrams. Again, exactly the same as we did with meters. So 1 million grams. And we know that 1 gram equals 1,000 milligrams. So we set this up to do our conversion. Again, we make sure that our units are going to cancel. So we put 1 gram down here, 1,000 milligrams up here. And if we multiply 1 million times 1,000, we get 1 billion milligrams. So we can do conversions. And the conversions are much easier, because all you have to do is know the prefix. You don't have to look up any odd conversion rates, like remembering how many ounces are in a pound or how many feet there are in a mile. So the conversions are always done by powers of 10. So let's finish up here with our summary. And what we have that we've looked at is that the metric system is the system that is used for science all over the world and in the rest of the world, other than the US pretty much, is used as the standard set of measurements. So if you're trying to find masses, people will weigh things and figure out masses in kilograms. They won't normally tell you things in pounds. If you're trying to get a certain amount of gas, yes, in the United States, we use gallons, but elsewhere they will use liters as the measure of volume. In order to get that. So all scientific work is done in metric units. And the conversions are much easier, because everything is based on powers of 10. So that concludes this discussion on the metric system. And we'll be back again next time for another topic in math help for science courses. So until then, have a great day, everyone. And I will see you in class.