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

Question

\(0.3\overline2\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), is

A. \(\frac{8}{25}\)

B. \(\frac{29}{90}\)

C. \(\frac{32}{99}\)

D. \(\frac{32}{199}\)

Answer 1

Let x = \(0.3\overline2\)

10x = \(3\overline2\) (i)

100x = \(32.\overline2\) (ii)

Now, subtracting (i) from (ii), we get 

100x – 10x = \(32.\overline2\,-3.\overline2\)

90x = 29

\(\times= \frac{29}{90}\)