MathDB

Sum of Repeating Decimals

Source: 2006 AIME A Problem 6

March 9, 2006

AMC

Problem Statement

Let

\mathcal{S}

be the set of real numbers that can be represented as repeating decimals of the form

0.\overline{abc}

where

a, b, c

are distinct digits. Find the sum of the elements of

\mathcal{S}