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Rationalizing Decimals (Posted on 2007-09-26) Difficulty: 3 of 5
Consider the rational number which in decimal form is .12345345345345...
It begins with two non-repeating digits followed by a block of 3 digits which repeats.

For the generalized repeating decimal .[a][b][b][b][b]...
Where [a] has n digits and [b] has m digits.

Find a general way to transform it into a rational number of the form p/r.

See The Solution Submitted by Jer    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Answer | Comment 6 of 8 |

The required rational number is given by:
 
p/r = (S*[a] + [b])/(10^n*S), where S = (10^m -1)

Edited on September 28, 2007, 7:29 am
  Posted by K Sengupta on 2007-09-27 06:04:11

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