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We're asked how many centiliters are in one dekaliter? So the first thing we want to
do is just think about how much is a centiliter relative to
a liter, and how much is a dekaliter relative to a liter? And I'll write the
prefixes down. And really, you should have
these memorized because you're going to see these prefixes
over and over again for different types of units. So the prefix, kilo, sometimes
[? ki-lo, ?] this means 1,000. If you see hecto,
hecto means 100. Deka means 10. If you have nothing, then
that just means 1. Let's put that there. Then if you have deci,
this means 1/10. If you have centi,
this means 1/100. If you have milli, this
means 1/1,000. So let's go back to what we
have. We have centiliters. Let me write this in
a different color. If you have a centiliter, this
is equal to 1/100 of a liter, Or you could say 1 liter for
every 100 centiliters, so you could also write it like this:
1 liter for every 100, or per every 100, centiliters. So we got the centi, now let's
think about the dekaliter. So the deka is right
over here. So a dekaliter means
10 liters. Or another way to say it is for
every 10 liters, you will have 1 dekaliter. Now, before I actually
work out the problem, what's going on here? We're going from a smaller
unit to a larger unit, so there are going to be many of
the smaller units in one of the larger ones. And we can do it
multiple ways. So we want to essentially
convert 1 dekaliter into centiliters. Now, we could just do it by
looking at this chart, or we could do it with the dimensional
analysis, making sure the dimensions work out. Let's do it the first way. So if you have one dekaliter,
how many liters is that? 1 dekaliter over here would be
the same thing as 10 liters. That's liters. We're assuming that our
unit is liters here. And then 10 liters is going
to be how many deciliters? It's going to be 100
deciliters, right? Because each of these is
10 deciliters, and you have 10 of them. So every time you go down,
you're going to be multiplying by a factor of 10. 100 deciliters is how
many centiliters? Well, 100 deciliters, each of
them is going to be worth 10 centiliters, so that's going
to be 1,000 centiliters. So we have our answer:
1 dekaliter is 1,000 centiliters. Now, the other way to do it is
you could convert a dekaliter to liters, and then convert
a liter to centiliters. So if we have one dekaliter--
and whenever you do unit things, just make sure
that it makes sense. Sometimes, people, instead of
multiplying, they would divide, and then they'd get,
oh, 1 dekaliter is equal to 1/1,000 of a centiliter. And they say, no, no, no, no. A dekaliter is a much larger
unit that a centiliter. So 1 dekaliter has to be
a bunch of centiliters. This should be a large number,
so you should always do that reality check whenever you're
dealing with units. Now, let's do it the dimensional
analysis way. We're starting with
one dekaliter. We want to convert
it to liters. So if you're converting it to
liters, you want the dekaliter in the denominator and you want
liters in the numerator. Now, how many liters
are 1 dekaliter? Well, you could say 10 liters
is equal to 1 dekaliter. So 1 dekaliter is equal
to-- these cancel out. 1 times 10 is 10 liters. Now, if we wanted to convert
this to centiliters, we're going to want the liters in the
denominator, and you want the centiliters in
the numerator. Now, how many centiliters are
there per liter? How many centiliters? Well, 1 liter is 100
centiliters. Centiliter is 1/100
of a liter. Notice, this and this are
the inverse statements. They're saying same the
exact same thing. 1 liter per 100 centiliters. Here, writing 1 liter
per 100 centiliters. We've just flipped it, but
they're giving the same information. And the reason why we flipped
it is so that the liters cancel out, and then we're just
left with 10 times 100 is 1,000 centiliters. And we are done!