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# Converting within the metric system

Sal shows conversions within the metric system. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

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.