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 \(x\).

\[ x = \frac{45}{99}\]