Question

The sum of 0.$\overline{3}$ and $0.\overline{4}$ is

(a)$\frac{7}{10}$

(b)$\frac{7}{9}$

(c)$\frac{7}{11}$

(d)$\frac{7}{99}$

Answer 1

Let $x=0.\overline{3}=\mathrm{0.333...}$----(1)
Multiplying both sides by 10, we get

$10x=\mathrm{3.33333...}$----(2)

Subtracting (1) from (2), we get

$10x-x=\mathrm{3.333..}-\mathrm{0.3333..}\Rightarrow 9x=3\Rightarrow x=\frac{3}{9}\therefore 0.\overline{3}=\frac{3}{9}$

Let $y=0.\overline{4}$ = 0.444...----(3)

Multiplying both sides by 10, we get

$10y=\mathrm{4.444..}$----(4)

Subtracting (3) from (4), we get

$10y-y=4.4444-0.4444\Rightarrow 9y=4\Rightarrow y=\frac{4}{9}\therefore 0.\overline{4}=\frac{4}{9}$

Sum of $0.\overline{3}$ and $0.\overline{4}=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}$

Hence, the correct answer is the option (b)