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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!