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

Question

\(23.\overline{43}\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), is

A. \(\frac{2320}{99}\)

B. \(\frac{2343}{100}\)

C. \(\frac{2343}{999}\)

D. \(\frac{2320}{199}\)

Answer 1

x = \(23.\overline{43}\) (i)

100x = 2343. \(.\overline{43}\) (ii)

Subtracting (i) from (ii), we get

100x – x = 2343.\(23.\overline{43} - 23.\) \(23..\overline{43}\)

99x = 2320

x \(= \frac{2320}{99}\)