To convert 0.82¯¯¯¯¯

Question

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 \( 0.82\overline{2} \) (which means it is \( 0.822222...\)) to a rational number, you should set \( x = 0.82\overline{2} \).

To eliminate the repeating part (the 2), you would multiply both sides of the equation by 10, since there is one digit before the repeating part (2). This gives:

\[ 10x = 8.22222... \]

Now you can use this equation along with the original \( x \) to eliminate the repeating decimal.

So, the number you'd multiply both sides by is 10.