How do you convert a basic recurring decimal into a fraction?

To convert a basic recurring decimal into a fraction, the most effective method involves defining the recurring decimal as a variable, usually represented by ( x ). After establishing this variable, you multiply it by a power of 10 that shifts the repeating part of the decimal to the left of the decimal point, allowing you to set up an equation for solving.

For example, if you have a recurring decimal like ( 0.666...), you would first let ( x = 0.666...). By multiplying both sides of the equation by 10 (a power of 10 appropriate for the number of decimal places in the repeating part), you would get ( 10x = 6.666...). This is where the key part comes in: now you have two equations:

1. ( x = 0.666...)
2. ( 10x = 6.666...)

By subtracting the first equation from the second, the repeating decimals will cancel out, leaving you with a simpler equation (in this case ( 10x - x = 6)), which can easily be solved for ( x ). The result will yield the fraction that represents the recurring decimal.

This method effectively captures the essence of converting recurring