To convert a repeating decimal like 0.82¯¯¯¯¯ to a rational number, we can set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by a power of 10 equal to the number of digits in the repeating decimal.
In this case, there are 2 repeating digits (82), so we would multiply both sides of the equation by 100 (10^2).
Therefore, the number we would multiply both sides of the equation by is 100.