Question

Match the following columns:

Column I		Column II
(a)	$\mathrm{\pi }$ is ...... .	(p)	a rational number
(b)	$3.\overline{1416}$ is ...... .	(q)	an irrational number
(c)	$0.\overline{23}$ = ....... .	(r)	$\frac{7}{30}$
(d)	$0.2\overline{3}$ = ...... .	(s)	$\frac{23}{99}$

(a) ......
(b) ......
(c) ......
(d) ......

Answer 1

(a) $\mathrm{\pi }$ is an irrational number.

(b) 3.141614161416... is a rational number because it is a non-terminating but repeating decimal.

(c) Let x = 0.23232323... ...(i)
$\therefore$ 100x = 23.232323... ...(ii)
Subtracting (i) from (ii), we get:
99x = 23
Or,
x = $\frac{23}{99}$

(d) Let x = 0.233333333.. ...(i)
$\therefore$ 10x = 2.33333333.. ...(ii)
We have:
100x = 23.333333333 ...(iii)
Subtracting (ii) from (iii), we get:
90x = 21
Or,
x = $\frac{21}{90}=\frac{7}{30}$