Question

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 \( 0.82\overline{82} \) (where \( \overline{82} \) indicates that "82" repeats indefinitely) to a rational number, you would set \( x = 0.82\overline{82} \).

Since the repeating part has 2 digits, you should multiply both sides by \( 100 \) (which is \( 10^2 \)) to move the decimal point two places to the right.

So you would multiply by \( 100 \):

\[
100x = 82.82\overline{82}
\]

This allows you to set up an equation that can eliminate the repeating part when combined with another equation derived from the original \( x \).