\(0.3\overline2\) when expressed in the form \(\frac{p}q\) (p, q ar

1.	\(0.3\overline2\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), isA. \(\frac{8}{25}\)B. \(\frac{29}{90}\)C. \(\frac{32}{99}\)D. \(\frac{32}{199}\)
Answer» 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 \(\times= \frac{29}{90}\)

\(0.3\overline2\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), isA. \(\frac{8}{25}\)B. \(\frac{29}{90}\)C. \(\frac{32}{99}\)D. \(\frac{32}{199}\)

Answer»

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

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