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/