00:01
Hey there.
00:02
In this problem, we have some dimensional analysis to do to allow us to convert from one unit to another, and we are given some equalities in the problem.
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We are told that one carrot, what diamonds are typically measured in, is equal to 0 .2 .00 grams.
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We are also given the density of diamond.
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So i'm going to write that as an equality also.
00:29
One centimeter cubed is equal to 3 .5.
00:34
5 -1 grams.
00:36
That's the density written as inequality.
00:39
All right, so let's go ahead and get started.
00:41
In letter a, we have a 5 .0 carrot diamond, and we want to know its volume.
00:53
What's its volume? well, remember, dimensional analysis is kind of going one step at a time.
00:59
It's like a little puzzle going from one step at a time to get from your starting point to where you're trying to go.
01:05
So if i have carrots, i see that i convert to grams because of my first equation, and then i convert from grams to volume using density.
01:16
So let's go ahead and do that.
01:18
My first equation, i want to put carrot on the bottom so that it will cancel.
01:24
So that means the 0 .200 grams goes in the numerator.
01:29
So carrot will cancel.
01:30
Right now i have the mass in grams, but i want the volume.
01:36
So i'm going to use the density now.
01:37
But i need to put the mass in the denominator.
01:40
So that grams will cancel.
01:42
That means one centimeter cubed goes in the numerator, and that will be the unit in my answer.
01:50
So grams cancel.
01:52
Now it's a calculator problem.
01:53
I'm going to take 5 times .2 and divide by 3 .51.
01:58
I need to round my answer to just two significant figures because 5 .0 only had two significant figures...