A student writes the repeating decimal as the infinite sum

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

A student writes the repeating decimal

0.\overline{4}

as the infinite sum

0.4 + 0.04 + 0.004 + \dots

. What is the common ratio

r

of this series? (a)

\dfrac{4}{10}

(b)

\dfrac{1}{9}

(c)

\dfrac{1}{10}

(d)

\dfrac{4}{9}