Metric and Unit Conversions

Date: 11/02/98 at 16:06:18
From: Jennifer Corvison
Subject: Metrics

I am having a hard time figuring out metric conversions. I need an 
explanation in words. Here are some examples:

   60 mi/hr = ______ ft/sec
   2 L = _____ oz
   7.68 kg = ____ lbs
   1816 g = _____ lbs
   5 m = _____ in
   3 qt = ___ L
   10 m(cubed) = _____ ft(cubed)
   3 dm = _____ ft
   1.4 lb = ___ g

Please help.

Date: 11/02/98 at 17:17:29
From: Doctor Rick
Subject: Re: Metrics

Hi, Jennifer. Here are a few tricks that I use to be sure I get 
conversions right.

First, you can write a conversion factor as a fraction that equals 1. 
For instance, I know that 1 pound = 454 g. I write this as:

  454 g
  ----- = 1
   1 lb

Second, multiply the measurement you are given by a conversion 
fraction. Write the fraction so that the units cancel. (You can think 
of a unit as a number you multiply by, and cancel units in a fraction 
as if they were numbers.) For instance, to convert 1816 grams to 
pounds, I write:

            1 lb
  1816 g * ----- = 4.0 lb
           454 g

The grams in the numerator cancel the grams in the denominator, so you 
are left with lb. If I write the fraction as I did above (in my first 
fraction), the units will not cancel. This is how I know whether I 
should multiply or divide.

Third, if you don't know the conversion factor that you need, you can
construct a "chain" of conversion fractions. For instance, here's how 
to convert 7.68 kg to pounds if I only remember how to convert grams 
to pounds. First I convert 7.68 kg to grams, then grams to pounds. 
Here is the full chain:

            1000 g    1 lb
  7.68 kg * ------ * ----- = 16.9 lb
             1 kg    454 g

Compound units work similarly. For instance, to convert 60 mi/hr to 
ft/sec, do this:

  60 mi   5280 ft    1 hr     1 min
  ----- * ------- * ------ * ------ = 88.0 ft/sec
   1 hr     1 mi    60 min   60 sec

See how miles, hours, and minutes all cancel. Similarly, when you 
convert m^3 to ft^3 (^ is how we customarily write "cubed" using a 
keyboard), you want to use the feet/meters fraction 3 times, because 
m^3 = m * m * m. If you don't know feet/meter (I don't), do this:

             100 cm     1 in    1 ft
  10 m^3 * ( ------ * ------- * ----- )^3 = 10 * 3.28^3 = 353.15 ft^3
               1 m    2.54 cm   12 in

If you can use a calculator and you master this technique, you only 
need to remember a few metric-English conversion factors, such as:

  1 inch = 2.54 cm
  1 lb = 454 grams
  1 liter = 1.06 quart

You also need to know the conversions between English units (3 feet in 
a yard, etc.), and the meaning of metric prefixes (kilo = 1000, 
centi = 1/100, etc.)

I hope this helps you.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/