MathDB
Fraction Approximation

Source:

December 20, 2005

Problem Statement

The number rr can be expressed as a four-place decimal 0.abcd,0.abcd, where a,b,c,a, b, c, and dd represent digits, any of which could be zero. It is desired to approximate rr by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to rr is 27.\frac 27. What is the number of possible values for rr?
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