Question

The decimal form of $\frac{1}{3}$ is .

• A. 0.3
• B. 0.6
• C. 0.3333...

Answer 1

The correct option is C 0.3333...

Given fraction is $\frac{1}{3}$.
$\frac{1}{3}$ = $\frac{1}{10}$ $\times$ $\frac{10}{3}$

$\Rightarrow \frac{1}{3}=\frac{1}{10}$ $\times$ $(3+\frac{1}{3})$

$\Rightarrow \frac{1}{3}=\frac{3}{10}+\frac{1}{30}$

$\Rightarrow \frac{1}{3}-\frac{3}{10}=\frac{1}{30}$

Smaller the value of ' $\frac{1}{3}-\frac{3}{10}$' , the closer is $\frac{3}{10}$ to $\frac{1}{3}$ .

Let's write $\frac{1}{3}$ as,

$\frac{1}{3}=\frac{1}{100}$ $\times$ $\frac{100}{3}$

$\Rightarrow \frac{1}{3}=\frac{1}{100}$ $\times$ $(33+\frac{1}{3})$

$\Rightarrow \frac{1}{3}=\frac{33}{100}+\frac{1}{300}$

$\Rightarrow \frac{1}{3}-\frac{33}{100}=\frac{1}{300}$

Since $\frac{1}{300}<\frac{1}{30}$, $\frac{33}{100}$, when compared with $\frac{3}{10}$, is closer to $\frac{1}{3}$ .

If we continue like this, we get

$\frac{1}{3}-\frac{3}{10}=\frac{1}{30}$

$\frac{1}{3}-\frac{33}{100}=\frac{1}{300}$

$\frac{1}{3}-\frac{333}{1000}=\frac{1}{3000}$

$\frac{1}{3}-\frac{3333}{10000}=\frac{1}{30000}$

........and so on.

The difference between the fractions $\frac{3}{10}$,$\frac{33}{100}$, $\frac{333}{1000}$, $\frac{3333}{10000}$ and $\frac{1}{3}$ gets smaller and smaller and we can make this difference as small as we want.

Therefore, we can write as $\frac{1}{3}$= 0.33333....