Question

Write the decimal as a fraction or mixed number.

$\mathbf{0}\mathbf{.}\overline{\mathbf{12}}$

Short answer

The fraction is $\frac{4}{33}$.

Step-by-step solution

Step 1. Given information

Consider, the decimal $0.\overline{12}$ provided in question.

Step 2. Calculation

Let $x=0·\overline{12}$

$x=0·121212.....$ …… (1)

Clearly, 12 is the only digit which is repeating in equation (1)

Multiply equation (1) by 100 on both sides

$100x=12·1212.....$ …… (2)

Subtract equation (1) from equation (2),

Therefore,

$\begin{array}{c}100x-x=(12\cdot \mathrm{1212.....})-(0\cdot \mathrm{121212.....})\\ 99x=12\\ x=\frac{12}{99}\\ x=\frac{4}{33}\end{array}$

Thus, the fraction number that can be formed is$\frac{4}{33}$.