Question

Match the following decimal forms to their correct $\frac{p}{q}$ form.

• A. $\frac{1}{3}$
• B. $\frac{41}{33}$
• C. $\frac{29}{198}$

Answer 1

Case 1:
Let us assume,
$x=0.\overline{3}$........ (i)

$10x=3.\overline{3}$..... (ii)

(ii) - (i)
$10x-x=3.\overline{3}-0.\overline{3}$
$9x=3$
$x=\frac{3}{9}$
$x=\frac{1}{3}$

Case 2:
Let us assume,
$x=1.\overline{24}$........ (i)

$100x=124.\overline{24}$..... (ii)

(ii) - (i)
$100x-x=124.\overline{24}-1.\overline{24}$
$99x=123$
$x=\frac{123}{99}$
$x=\frac{41}{33}$

Case 3:
Let us assume,
$x=0.1\overline{46}$........ (i)

$10x=1.\overline{46}$..... (ii)
$1000x=146.\overline{46}$..... (ii)

(iii) - (ii)
$1000x-10x=146.\overline{46}-1.\overline{46}$
$990x=145$
$x=\frac{145}{990}$
$x=\frac{29}{198}$