In the conversion process for recurring decimals, what step follows subtracting the two equations?

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