Fractions and Measurement

Date: 04/11/97 at 12:11:09
From: Ed Stanley
Subject: Fractions and Measurement

We are studying measurement in school and I have noticed there is 
nothing smaller than an inch with a name unlike 1/2, 1/4,and 1/8 inch. 
Are there any names? Can you give me a list of fractions until 
.0000000---until 51 zeros?

Date: 04/11/97 at 15:12:55
From: Doctor Steven
Subject: Re: Fractions and Measurement

Rational numbers are infinite in number; there are an infinite number
of them between any two points.  Take the fractions between 0 and 1 
for instance we have : 1/1, 1/2, 1/3, 1/4, ....  We can keep going on 
forever and we will still have more to count.  

On a ruler, we tend to use powers of 2 in the denominator: 

  1/2^1 = 1/2   = 0.5
  1/2^2 = 1/4   = 0.25
  1/2^3 = 1/8   = 0.125
  1/2^4 = 1/16  = 0.0625
  1/2^5 = 1/32  = 0.03125
  1/2^6 = 1/62  = 0.015625
  1/2^7 = 1/128 = 0.0078125
 
Each time we increase the exponent by about 3, we add another decimal 
place, more or less.  So we'd have to get up to about 1/2^150 to 
get 50 zeros in front of the decimal place.  

We would never use fractions this small, so we don't give them names. 

However, there are some traditional units that are smaller than 
an inch.  At one of our favorite sites about units, 

  How Many? A Dictionary of Units
  http://www.unc.edu/~rowlett/units/

we find the 'line':

  line (li) [1] 
  a traditional unit of distance equal to 1/12 inch (about 2.1167
  millimeters). For measuring the thickness of buttons, there is
  also a smaller line equal to 1/40 inch (0.635 millimeter). The
  line is called the ligne (see above) in French, the linea in
  Spanish, the linie in German, and the liniya in Russian. 

  line [3] 
  a unit of distance equal to 1/14 inch, used in printing and
  advertising. This usage is short for agate line. 

You can also find there descriptions of units called 'points' 
and 'picas', which are used by printers. 

Hope this helps!

-Doctor Steven,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/