Terminating and Repeating Decimals

Date: 04/20/2003 at 22:13:26
From: Lil Ree
Subject: Repeating decimal

Which one of these could be written as a repeating decimal:

a. 3/8
b. 7/16
c. 1/2
d. 5/6

To me, all of these could be repreating decimals.

Date: 04/20/2003 at 22:50:53
From: Doctor Peterson
Subject: Re: Repeating decimal

Hi, Lil.

You're right! Every fraction CAN be written as a repeating decimal; 
those that can be written as terminating decimals can ALSO be 
written as repeating decimals with either a 0 or a 9 repeating:

  1/2 = 0.5 (terminating)
      = 0.50000000000... (repeating 0)
      = 0.49999999999... (repeating 9)

Probably the intent of the question, though, was "which CANNOT be 
written as a terminating decimal?" that is, "which can ONLY be 
written as a repeating decimal?" If you try writing each of them as a 
decimal, you will find which one HAS to repeat.

There is also a fairly simple way to tell at a glance (or at least 
without actually dividing) whether any given fraction terminates. 
This depends on the factors of its denominator.

If you have any further questions, feel free to write back.

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