0.001 bar​ when expressed in the form p/q (p, q are integers, q ≠ 0), is ​

Question

\(0.\overline{001}\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), is

A. \(\frac{1}{1000}\)

B. \(\frac{1}{100}\)

C. \(\frac{1}{1999}\)

D. \(\frac{1}{999}\)

Answer 1

x = \(0.\overline{001}\) (i)

\(1000\times = 001.\overline{001} - 0.\overline{001}\)

999x = 1

\(\times = \frac{1}{999}\)