♪♪ In this segment of "Physics in Motion", we're gonna cover two important ways in which scientists can talk amongst themselves. Generally, science operates as a global community that relies upon collaboration and review. So scientists have developed two systems of measurement that allow them to communicate more effectively. One is called the SI System, which stands for the French phrase, Systeme Internationale. And the other is a kind of shorthand, called Scientific Notation. The SI System defines and sets standards for various measurements, so everyone is measuring the same way. It uses the metric system, which the French came up with about 300 years ago. The Metric System uses units, like meters and kilograms, to describe quantities, durations, temperatures, and other things that need measuring. Over the years, other countries began to use the French standards. Eventually, they established the SI, which was first published in 1960, and it made scientific progress much easier. You know how Legos have units, like these, that you can build on? So does the SI. They're called Base Units. There are seven of them. Meter, kilogram, seconds, ampere, candela, mole, and kelvin. Some are familiar, of course. Others, like the ampere and candela, you may not have heard about. But you will as we work through this series. In some equations, we can combine base units to provide more detailed information about what we're measuring. We call those Derived Units. If you look at how far a car has gone, in meters, in a certain amount of time, in seconds, we see that the units come together to tell us the speed of the car in meters per second. This is a Derived Unit. There's more information about Derived Units in your Unit 1 Toolkit. In the United States, we don't generally use the metric system for everyday measuring. We use the Imperial System of measurement, which uses feet, inches, pounds, and so on. But American scientists use SI units for their work. We can convert back and forth between SI and Imperial units using conversion factors, which are multipliers that allow us to convert a quantity expressed in one kind of unit into an equivalent value expressed in another. Here's how that works. Let's look at converting from Imperial to Imperial, first. We know that 12 inches equals 1 foot. We can represent this as 12 inches over 1 foot. This is our conversion factor. And we can use that to convert a number in feet to inches. How many inches are in 3 feet? We start by writing down 3 feet, and multiplying it by our conversion factor, 12 inches over 1 foot. Our feet units cancel, leaving us with our answer, 36 inches. But what if we wanna go from metric to Imperial? Let's do a problem together where we can do that. Let's say we wanna convert 24 centimeters into feet. First, write down the number we have, which is 24 centimeters. Next, multiply that number by a conversion factor. You may already know it, or you can look it up. Our conversion factor is 1 inch equals 2.54 centimeters. That will allow us to cancel out the units that are the same. In this case, centimeters. Remember that when you cancel, the units must appear on both sides of the dividing line. When you cancel out the centimeters, you're left with inches. But remember, we want to find our answer in feet. So you have to add another conversion factor to convert inches into feet. That conversion factor is 1 foot to 12 inches. When you cancel out your inches, you're left with feet, what we're solving for. Your last step is simple. You just multiply all of the numerators and divide by all the denominators. This will give you your answer, which tells us 24 centimeters is 0.79 feet. Now, there's something else really useful you can do, using the SI and metric quantities. If you want to show a metric quantity raised to some 10th power, you can add a prefix to the name. Here's a chart of the prefixes we use to do that. Let's take a look at a few. Mega is a million. So a megaton is a million tons. Milli is a thousandth. So a millimeter is a thousandth of a meter, and so on. And there are some pretty obscure ones too. Who knew there was a yotta, which is a quadrillion of something? Or a zepto, which is a sextillionth. But you can see how useful these prefixes are when we talk about quantity. What about if we want to convert a metric quantity to another metric quantity? Is there a shorthand for that? There is. You can do it by moving the decimal point. Let's take a kilometer, 1,000 meters. If you want to know how many meters are in 3 kilometers, we move the decimal the number of zeroes there are in 1000. So there's three places to the right, 3000 meters. There's a little phrase we use to help remember the decimal rules. King Henry Died By Drinking Chocolate Milk. Here, listen to this. It'll help you out. 'K' stands for kilo. 'H' is hecto. 'D' is for deca. 'B' is for base unit. 'D' stands for deci. 'C' stands for centi. And 'M' stands for milli. So those are the basics of the SI system. The base and derived units, prefixes and decimal points. There's another kind of shorthand language that scientists use for numbers that are too large or too small to write out. It's called scientific notation. Here's one place where it comes in handy. Astronomers estimate that there are between 200 billion and 400 billion stars in our galaxy. But what if we needed to write 400 billion in a calculation? Like if we wanted to know how many stars are in 100 galaxies? That would be 400 billion times 100, or 4 followed by 13 zeroes. Not a great plan, is it? Your calculator probably can't even handle that. Instead, you can write that same huge number using scientific notation. It would look like this. 4.0 times 10 to the 13th. That still means 4 followed by 13 zeroes. Same amount, shorter way to write it. When we write in scientific notation, we start with a number greater than or equal to 1, and less than 10, followed by 10 raised to a power. The little number to the right is the power. It is a positive power if you're talking about a number greater than 1, like our 4 times 10 to the 13th star. A negative integer power means you're talking about a number less than 1. For instance, 4 times 10 to the negative 13th power is the same thing as 0.0000000000004. Let's look at how we convert a number into scientific notation, step by step. The first thing is to find the decimal. Let's look at this number. 254,334,400. See the decimal to the right of the ones place? To put that in scientific notation, you move that decimal to a place where you have a number greater than or equal to one, but less than 10. That would be the 2. So let's count how many places we move the decimal. One, two, three, four, five, six, seven, and eight. And now, we write our number as 2.543344 times 10 to the 8th. And that's scientific notation. Let's do one more. This time, with a number less than 0. Let's say our number is 0.000054. Remember, we have to find a number greater than or equal to one, and less than 10. To get there, we move the decimal to the right. This time, one, two, three, four, five spaces. Our number is less than 1, so the power is negative. In scientific notation, we have 5.4 times 10 to the negative 5. So you can see why scientific notation comes in handy when we're dealing with some of the very small and very large quantities that we use in physics? That's it for this segment of "Physics in Motion." We'll see you next time. For more practice problems, lab activities and note-taking guides, check out the "Physics in Motion" toolkit.