Question

To convert 0.82 (repeating decimal) 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 \( 0.82\overline{82} \) to a rational number, you would set \( x = 0.82\overline{82} \). Since the repeating part (the "82") has two digits, you would multiply both sides of the equation by \( 100 \).

This gives you:

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

Now you can set up an equation to isolate \( x \). This method allows you to eliminate the repeating part by subtracting the two equations.