Consider the recurring decimal expansion x = 0

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Consider the recurring decimal expansion x=0.abc‾,x = 0.\overline{abc}, where a, b, ca,\,b,\,c are digits and the bar indicates that the block abcabc repeats without end. Answer the following. (i) Prove that x=abc999x = \dfrac{abc}{999}. (ii) Hence express 0.527‾0.\overline{527} as a fraction in its simplest form.

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