Ace Your Maths Goals 2026 – Dive into the Ultimate GCSE Practice Exam Adventure!

To convert a recurring decimal into a fraction, you typically start by letting the decimal be represented as a variable, say \( x \). For example, if we have a recurring decimal like \( 0.666...\), we can express it as follows:

1. \( x = 0.666...\)

2. Multiply both sides of the equation by a power of 10 that aligns with the position of the recurring part. In this case, \( 10x = 6.666...\).

3. Next, subtract the first equation from the second equation:

\( 10x - x = 6.666... - 0.666...\)

Simplifying this yields:

\( 9x = 6\).

At this stage, the next step involves isolating \( x \). To achieve that, you need to divide both sides of the resulting equation by the difference between the two sides, which in this case is \( 9 \).

This method of subtracting the two equations allows us to eliminate the decimal part, making it easier to form a simple fraction. Therefore, dividing by the difference between both sides is the crucial approach following the subtraction step in the recurring decimal conversion process. This logical progression is