Question

Write the decimal as a fraction or mixed number.

$\mathbf{2}\mathbf{.}\overline{\mathbf{707}}$

Short answer

The fraction is $\frac{2705}{999}$.

Step-by-step solution

Step 1. Given information

Consider, the decimal $2.\overline{707}$ provided in question.

Step 2. Calculation

Consider $\text{2}·\overline{707}\text{= 2 +}\left(0·\overline{707}\right)$

But $0·\overline{707}\text{=}\frac{707}{999}$.

Therefore,

$\begin{array}{c}\text{2}\cdot \overline{707}=2+\left(\frac{707}{999}\right)\\ =\frac{\left(2\times 999\right)+\left(707\right)}{999}\\ =\frac{2705}{999}\end{array}$

Thus, the fraction number that can be formed is $\frac{2705}{999}$.