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### Metric Unit Conversions

```
Date: 08/21/2001 at 21:59:26
From: Damian Montgomery
Subject: Changing metric units

How do you know when you should multiply or divide in these
conversions?
```

```
Date: 08/22/2001 at 14:20:18
From: Doctor Ian
Subject: Re: Changing metric units

Hi Damian,

Actually, when converting units, you're always multiplying by 1 (which
is why you can do it without changing the meaning of anything).  For
example,

1 in       1 ft
3 cm * -------- * ------ = ?
2.54 cm    12 in

^         ^
|         |
This is    So is this.
the same
as '1'.

Note that you can treat the units just as if they were numbers; and
since the order of multiplications is irrelevant, you can group them
all at the end

1 in       1 ft     3 * 1 * 1   cm * in * ft
3 cm * -------- * ------ = --------- * --------------
2.54 cm    12 in    2.54 * 12   cm * in

Once they're grouped like that, you can cancel them, just as you would
cancel numbers that appear in both the numerator and denominator of a
fraction:

x    x
1 in       1 ft     3 * 1 * 1   cm * in * ft
3 cm * -------- * ------ = --------- * --------------
2.54 cm    12 in    2.54 * 12   cm * in
x    x

= 3 / (2.54 *12) ft

So, when you need to convert something, how do you decide whether to
multiply by

21.2 blurgs
-------------
0.015 zibbles

or

0.015 zibbles
-------------      ?
21.2 blurgs

The answer depends on which unit you need to cancel. If you're
starting with zibbles, the first one will give you

zibbles * blurgs
----------------
zibbles

which is the same as blurgs; but if you're starting with blurgs, then
the second one will give you

blurgs * zibbles
----------------
blurgs

which is the same as zibbles.

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Terms/Units of Measurement

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