Question

Express the following in the form of $\frac{p}{q}$, where $p$ and $q$ are integers.

$\mathrm{0.555...}$

• A. $\frac{15}{9}$
• B. $\frac{5}{19}$
• C. $\frac{5}{9}$
• D. $\frac{3}{9}$

Answer 1

Answer: (C)

$\frac{5}{9}$

Let $q=\mathrm{0.555...}=0.\overline{5}$ ......... $\left(i\right)$

$10q=\mathrm{5.555...}=0.\overline{5}$......... $\left(ii\right)$

Subtracting $\left(i\right)$ from $\left(ii\right)$, we get

$10q-q=5$

$\Rightarrow q=\frac{5}{9}$
Hence, $\mathrm{0.555...}=\frac{5}{9}$