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### Unit Conversions - Metric System

```
Date: 7/29/96 at 15:51:44
From: Anonymous
Subject: Conversions to and from Metric Units

Perform the following conversions by multiplying or dividing by the
appropriate power of 10.

1. 3.25 cm to millimeters
2. 9.24 km to meters

Perform the following conversions. Use a calculator.

3. 1,000 mi to kilometers
4. 7.68 kg to pounds
```

```
Date: 7/29/96 at 20:8:32
From: Doctor Jerry
Subject: Re: Conversions to and from Metric Units

My favorite way of doing conversions is to use "unit cancellation."
I'll illustrate this by working out questions 1 and 3.  If you find
this method interesting and useful, perhaps you can work out questions
2 and 4.

Think of a fact like 1 mile is the same as 5,280 feet as a ratio;
either (1 mile)/(5280 feet) or (5280 feet)/(1 mile).  Each ratio acts
like the number 1 since the two things are equivalent measures. We use
the ratio that allows us to convert units as we wish. Here's question
3.

1000 miles    5280 feet   12 inches   2.54 cm    1 meter      1 km
---------- x  --------- x --------- x ------- x  ------- x -----------
1         1 mile       1 foot    1 inch      100 cm   1000 meters

Notice that the two miles units cancel, the two feet cancel, the
inches cancel, the cm cancels, and the meters cancel.  The remaining
unit is km, which is what we want. All that remains is to calculate
1000*5280*12*2.54/100/1000 = 1609.344 km. Now, note that I did this
in a long way - I wanted to demonstrate just how to use this "unit
cancellation" method. If you knew ahead of time that for every mile
we have 1.6 kilometers, you could have done the problem in one step
instead of five.  Can you see how that would go?

For the first question,

3.25 cm   10 mm
------- x ----- = 32.5 mm.
1       1 cm

Good luck on the other questions.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

```
Associated Topics:
Middle School Terms/Units of Measurement

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