Finding Fractions on a Ruler

Date: 08/16/99 at 01:17:09
From: Brian Strope
Subject: Defining Fractions of an Inch

Dear Dr. Math,

My question is simple. I want to know how to read all the measurements 
within 1 inch. We know that every line on a ruler or tape measure 
(whichever) has a fractional meaning. I want to learn how these 
fractions are arranged. 

I hope you understand what I mean by all fractions in an inch. 
Example: where is 7/8 of an inch compared to 5/16 of an inch on a tape 
measure? I know where the basic measurements are, such as 1/4, 1/2, 
and 3/4 of an inch. It's just the other measurements that I don't get.

Thank you.
F. Brian Strope

Date: 08/16/99 at 11:17:58
From: Doctor Peterson
Subject: Re: Defining Fractions of an Inch

Hi, Brian.

There's a lot of information hidden in a ruler, and it can take some 
practice to find it all.

We have a very complete explanation of reading a ruler here in our 
archives:

   Reading a Ruler
   http://mathforum.org/library/drmath/view/58333.html   

I'll give you a simpler, quick answer that may meet your needs. Here's 
a ruler showing 16ths, with the meaning of each mark indicated:

   0                                                               1
   |                              1/2                              |
   |                               |                               |
   |              1/4              |              3/4              |
   |               |               |               |               |
   |      1/8      |      3/8      |      5/8      |      7/8      |
   |       |       |       |       |       |       |       |       |
   |  1/16 |  3/16 |  5/16 |  7/16 |  9/16 | 11/16 | 13/16 | 15/16 |
   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
   +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Some rulers only go to eighths, and it might be easier to start with 
that:

   0                                                               1
   |                              1/2                              |
   |                               |                               |
   |              1/4              |              3/4              |
   |               |               |               |               |
   |      1/8      |      3/8      |      5/8      |      7/8      |
   |       |       |       |       |       |       |       |       |
   +-------+-------+-------+-------+-------+-------+-------+-------+
   0      1/8     2/8     3/8     4/8     5/8     6/8     7/8      1

As the marks go down in size, the denominator of the fraction doubles. 
The biggest mark between two inches is the half; between that and 
either inch mark the next largest mark is the quarter inch; and so on. 
To find eighths, just go down the scale finding 1/2, then 1/4, then 
1/8. All the marks that are that size or bigger are eighths: 1/8, 2/8 
(which is the same as 1/4), 3/8, 4/8 (which is the same as 1/2), 5/8, 
and so on. If you want, you can just count all the marks that are the 
same size, counting by odd numbers: 1/8, 3/8, 5/8, 7/8.

Try doing the same thing on the 16ths ruler above; the only hard part 
will be to ignore the smaller 16ths marks while you're looking for 
8ths. To find 5/8, for example, find which size marks are 8ths, then 
count 1, 3, 5/8 until you find it.

Now you should be able to work out 32nds yourself:

 0                                                               1
 |                              1/2                              | /2
 |                               |                               |
 |              1/4              |              3/4              | /4
 |               |               |               |               |
 |      1/8      |      3/8      |      5/8      |      7/8      | /8
 |       |       |       |       |       |       |       |       |
 |  1/16 |  3/16 |  5/16 |  7/16 |  9/16 | 11/16 | 13/16 | 15/16 | /16
 |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
 | 1 | 3 | 5 | 7 | 9 | 11| 13| 15| 17| 19| 21| 23| 25| 27| 29| 31| /32
 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

If you need any more help, feel free to write back.

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