Unit Conversions

Date: 11/16/95 at 11:44:15 
From: L. Johnson
Subject: Math question

How many centimeters are in 1,200,345 yards?

Karen Goings

Date: 11/19/95 at 15:32:8
From: Doctor Jeremy
Subject: Re: Math question

Here's a technique to figure out almost any such unit-conversion 
problem, using fractions.  You treat the units (yard, foot, cm) as if 
they represented some numbers, the actual values of which you don't 
know.

You can find out (by looking it up in an appropriate book like an 
almanac) that there are 3 feet in a yard.  So you make a fraction

	3 feet
	------
	 yard

Since "3 feet" and "1 yard" are the same, the whole fraction is equal to 
1.

You also know that there are 30 centimeters (approximately) in a foot.
This gets you

	30 cm
	-----
	foot

Now since both of these fractions are just equal to 1, multiplying a 
value by them does not change that value.  So

                  1,200,345 yards   3 feet   30 cm
1,200,345 yards = --------------- x ------ x -----
                         1           yard    foot

   1,200,345 * 3 * 30 * yard * foot * cm
 = -------------------------------------
               yard * foot

And cancelling the extra yard and foot, and doing the multiplication, 
you get

108,031,050 cm

You can do this with almost any sort of units; in physics and chemistry
classes it comes in very handy.

-Doctor Jeremy,  The Geometry Forum