00:02
Hi there.
00:03
In this question, we have four conversions to complete.
00:07
So we will use dimensional analysis to set these up.
00:10
So in letter a, we have 1 .65 kilometers.
00:14
And our goal is to convert this to meters.
00:17
So we need an equality between kilometers and meters.
00:21
Well, in one kilometer, there are 1 ,000 meters, because the prefix kilo means 10 to the third.
00:30
So it takes 1 ,000 meters to equal 1 kilometer.
00:35
With kilometer in the denominator, that cancels.
00:38
And calculating our answer gives us 1 ,650 meters.
00:49
All right, for letter b, we're trying to convert from milligrams to kilograms.
00:55
So we have 4 ,598 milligrams.
01:00
Well, millie means 10 to the negative third, while kilo means 10 to the positive third.
01:06
So there's a difference of 10 to the 6th between them.
01:10
Again, that's because kilo equals 10 to the third, milly equals 10 to the negative third.
01:19
So again, the difference is 10 to the 6th.
01:21
So it takes 1 times 10 to the 6th of the smaller unit, the milligram, to equal 1 kilogram.
01:30
And milligrams will cancel.
01:32
This gives us an answer of 0 .00440.
01:37
And since we had the four significant figures to start with, we want to make sure we still have those four significant figures in our answer.
01:50
Okay, for our next one, we are working with an english to metric conversion, but we are given some information here in the problem to help us out with that.
02:00
So we're starting with 126 feet, and in my first conversion, i'm going to convert from feet to inches because they tell us there are 12 inches and a foot.
02:11
Feet will cancel and now i'm in inches.
02:15
So in my next step i'm going to convert from inches to centimeters because we're told that there are 2 .54 centimeters in an inch.
02:25
All right.
02:26
So now we have centimeters and we want meters.
02:29
So i need a metric conversion and that is there are 100 centimeters in one meter.
02:37
All right.
02:38
We are ready to calculate our answer because the only unit remaining is meters...