Converting recurring decimals

When converting between recurring decimals and fractions, you will normally be expected to show a complete algebraic method.

Converting a recurring decimal to a fraction

$$0.45454545...$$

Let $x$ represent the recurring decimal.

$$x=0.45454545...$$

Multiply $x$ by a power of 10 equal to the number of digits that repeat. There are two repeating digits so we will use ${10}^2$, or 100.

$$100x=45.454545...$$

Subtract the original equation from the new one to eliminate the repeating part.

$$99x=45$$

Solve for $x$.

$$x=\frac{45}{99}$$