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Converting Millimeters to Inches and Back

Date: 03/14/2003 at 15:23:23
From: Fred
Subject: Convert millimeters to inches and inches to millimeters

I would like to see how to calculate without a chart.


Date: 03/14/2003 at 16:55:39
From: Doctor Ian
Subject: Re: Convert millimeters to inches and inches to millimeters

Hi Fred, 

By definition, 1 inch is the same as 2.54 centimeters. So it's the
same as 25.4 millimeters.  

So if you have a measurement in inches, you can multiply by 25.4 to
get the same measurement in millimeters. To go the other way, you'd
divide instead of multiplying. 

For example, if something is 6 1/2 inches long, that's

  6.5 * 25.4 = 165.1 millimeters

Conversely, if something is 165.1 millimeters long, that's

  165.1 / 25.4 = 6.5 inches

Since inches are often expressed using fractions, you may have to
convert from fractions to decimals before you can do this. You can
work out the denominator by starting from 1/2:

  1/2 = 0.5

Then divide by 2 to get the others. You can add zeros on the right and 
forget about the decimal point, to make things easier. 

  1/2 = 0.5

  1/4 = 0.50/2   = 0.25       (because 25 is half of 50)

  1/8 = 0.250/2  = 0.125      (because 125 is half of 250)

 1/16 = 0.1250/2 = 0.0625     (because 625 is half of 1250)  

But now we're getting back to something like a chart, aren't we?

Usually, people just memorize the decimal equivalents

  1/2 = 0.5         1/4 = 0.25         1/8 = 0.125

So, as an example, let's say that something is 6 3/8 inches. That's 

    6 3/8 

  = 6 + 3/8

  = 6 + 3 * (1/8)

  = 6 + 3 * (0.125)

  = 6 + 0.375

Now, there's an easier way to do this. Note that 3/8 is 1/8 short of
1/2. (This is easier to see if you're actually looking at a ruler.) 
So to figure out 3/8, just subtract 1/8 from 1/2, 

  3/8 = 1/2 - 1/8

      = 0.500 - 0.125

      = 0.375                 (Because 500 - 125 = 375) 

For 5/8, add 1/8 to 1/2.  For 7/8, subtract 1/8 from 1.  And so on. 

(Or, you could use a calculator. But it's always good to know that
you can get along without one, if you have to.) 
 
Let's look at one more example. Suppose we know that something is 170
millimeters long. In inches, that's 

  170 / 25.4 = 6.69 inches

But suppose you'd like this expressed in fractional inches. What I'd
do is start by breaking 0.69 into 1/2 plus something else:

  0.69 = 0.50 + 0.19

Now, 0.19 is kind of close to 0.25, so I can do the same thing again:

  0.69 = 0.50 + 0.25 - 0.06

And 0.06 is pretty close to 1/16.  So 

       ~
  0.69 = 1/2 + 1/4 - 1/16

       = 8/16 + 4/16 - 1/16

       = 11/16

(The '~' over the '=' means 'approximately equals'.) 

Does this help?

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

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