Converting within the metric system

Convert 51.8 decimeters to kilometers. So let's just think about what decimeters means in terms of meters, and then we can think about what kilometers mean in terms of meters, and then convert them. So we're going to start with 51.8 decimeters. Now, as a starting point, just to keep things simple, we're going to convert them into meters, because this prefix tells us a lot about how many meters this is. So if we want to convert it into meters, our units are going to have to be meters per decimeter. And we need this because this decimeter and that decimeter are going to cancel out, and we're going to be just left with meters. Now 1 meter is how many decimeters? Well, the prefix deci means 1/10. So 1 decimeter is 1/10 of a meter. Or another way of thinking about it is there are 10 decimeters for every meter. This is a smaller unit. 10 of these make up 1 of these, or 1/10 of a meter per decimeter, which is exactly what that is telling you. 1/10 of a meter. Now if you multiply these two things, what do we get? Well, the decimeters cancel out, and we divide 51.8 by 10. Multiplying by 1/10 is the same thing as dividing by 10. So this is going to be equal to 51.8 divided by 10. The decimal's just going to move to the left. It's going to be 5.18. So this is going to be 5.18 meters. And you should always do a reality check. Did it make sense? Does it make sense that 51 decimeters are equal to 5 meters? Well, sure. It should go down. We're going from a smaller unit to a larger unit, so we should have fewer of that larger unit to make the same distance in this case. A meter is a unit of length. Now, we're at 5.18 meters, and we want to now convert it to kilometers. So we're going to want meters in the denominator and kilometers in the numerator. Why? Because this meter and that meter will cancel out. Now, how many meters make up a kilometer? The kilo tells us 1,000. That is 1,000 meters. So 1,000 meters are equal to 1 kilometer. So if we were to multiply this, the meters cancel out and we'll just be left with kilometers. And multiplying something by 1/1,000 is the exact same thing as dividing by 1,000, and that makes sense. We should get a smaller number here because we're going from a smaller unit to a larger unit. So we're going to need a much smaller amount of the larger unit. So this is going to be equal to 5.18/1,000 kilometers. Now, the easy way to do this, if we take 5.18/10 is equal to-- we just move the decimal one to the left. It's going to be equal to 0.518. If we take 5.18 and divide it by 100, we're going to take the decimal two to the left. So one, two, we're going to have to add a zero here. So it's going to be 0.0518. And if we take 5.18 and we divide by 1,000, we're going to move the decimal three to the left. So we'll just do it. So if we start with 5.18-- the decimal started here-- we're going to go one, two, so that's one zero, and then three. And that's where the decimal is going to sit there. So this is Or another way, this is a little over 5/1,000. This right here is 5/1,000. It's a little bit more than that. So our final answer: 51.8 decimeters is equal to 0.00518 kilometers. And always do a reality check. Does that make sense? Well, sure. We're going from a really small unit here, a bunch of a small unit, to a very small amount of a large unit. It makes sense. It makes sense that this number goes down while the actual unit becomes larger.