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### Metric System Conversions

```
Date: 09/24/98 at 21:14:42
From: Nikki
Subject: Metric System Double conversions

I need help with the metric system using double conversions. For
example:

How many centimeters are in 14.25 decameters?
How would I solve that using a two-step process?

Thanks.
```

```
Date: 09/25/98 at 08:30:05
From: Doctor Rick
Subject: Re: Metric System Double conversions

Hi, Nikki. I'll show you a technique I use to be sure I get conversions
right.

You want to convert dekameters to centimeters. (Or do you mean
decimeters? I'll assume dekameters, since maybe you're learning a
different spelling.)

There is no point in memorizing this conversion factor. All you have to
remember is a table of prefixes:

...
deka  = 10
deci  = 1/10
centi = 1/100
milli = 1/1000
...

From this table, you can extract the information you need:

1 dekameter = 10 meters
100 centimeters = 1 meter

These can be written as fractions that equal 1:

1 dam   100 cm
----- = ------ = 1
10 m     1 m

Now we start with 14.25 decameters, so we multiply by a fraction with
dekameters in the denominator, so the dekameters will cancel (just as
if they were numbers). That means I must invert the first fraction:

10 m
14.25 dam * ----- = 142.5 m
1 dam

Then do the same to convert m to cm. This time I don't need to invert
the fraction, because meters are already in the denominator.

100 cm
142.5 m * ------ = 14,250 cm
1 m

There's your answer in two steps. What I usually do is to combine the
steps into one "chain of ones", like this:

10 m   100 cm
14.25 dam * ----- * ------ = 14,250 cm
1 dam     1 m

Just check that the units (dam and m) cancel, so that only cm are
left. That shows that you did the conversion correctly.

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

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