Enigma 1182: Recurring decimals
1 February 2016
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From New Scientist #2338, 13th April 2002 [link]
Some fractions expressed as decimals consist of a decimal point followed immediately by a set of digits that recurs ad infinitum: for example 2/37 = 0.054054054…
In this example the digits that form the fraction and the recurring decimal are all different from each other, but there are only six of them (2, 3, 7, 0, 5, 4).
Your task is to find another fraction written in its simplest form that when expressed as a decimal consists of a decimal point followed immediately by a set of digits that recurs ad infinitum. The digits that form the fraction and the recurring decimal must all be different from each other and there must be nine of them.
What is the fraction?