To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)

Answer 1

To convert the repeating decimal \( 0.82\overline{2} \) to a rational number, you would set \( x \) equal to \( 0.82\overline{2} \).

The repeating part has "2" repeating. Therefore, you should multiply both sides of the equation by \( 10 \) to move the decimal point one place to the right.

This gives: \[ x = 0.82\overline{2} \] \[ 10x = 8.2\overline{2} \]

Next, you can then multiply both sides by \( 10 \) again (for two digits, since you have "82" before the repeating decimal) to eliminate the repeating decimal: \[ 100x = 82.\overline{22} \]

From here, you can set up the equation to eliminate the repeating part. So, you effectively substitute \( 10 \), but depending on how you wish to structure it, you would also use \( 100 \) to remove the repeat after adjusting, based on the specifics of the problem.

Thus, the answer is that you multiply both sides of the equation by \( 100 \).