To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point) Responses 100 100 1,000 1,000 10 10 999

Answer 1

To convert the repeating decimal \( x = 0.264\overline{264} \) to a rational number, you will want to eliminate the repeating part. Since the repeat is 3 digits long (264), you can multiply both sides of the equation by 1000.

Thus, you set up the following:

1. Let \( x = 0.264\overline{264} \).
2. Multiply both sides by 1000:

\[ 1000x = 264.264\overline{264} \]

So, the correct answer is \( 1,000 \).