When converting a complex recurring decimal to a fraction, what do you do after letting x equal the decimal?

When converting a complex recurring decimal to a fraction, the correct next step after letting ( x ) equal the decimal is to multiply ( x ) by a power of 10 that shifts the non-repeating part of the decimal past the decimal point. This is crucial because it allows you to align the recurring part of the decimal in such a way that when you subtract the two equations, you can eliminate the repeating decimal.

For example, if your decimal is 0.1(23), you would let ( x = 0.1232323...). To shift the non-repeating part (which is 0.1) past the decimal point, you can multiply ( x ) by 10, giving you ( 10x = 1.232323...). This alignment helps in creating a situation where you can set up an equation that subtracts the two forms of ( x ) to isolate the repeating part.

The other methods suggested do not efficiently set up the necessary subtraction. Option A, dividing by the non-recurring part, would not yield a usable form for creating a fraction. Option C, adding two fractions together, does not pertain to the process of converting a decimal to a fraction. Option D,