Question

To convert 0.264 (264 is repeated) to a rational number, you would set x equal to 0.264 and then multiply both sides of the operation by what number?

1,000
10
999
100

Answer 1

To convert the repeating decimal \( x = 0.264264264\ldots \) to a rational number, you want to find a multiplier that shifts the decimal place of the repeating part.

In this case, the repeating part "264" has three digits. To eliminate the repeating part, you should multiply both sides of the equation by \( 1000 \). This moves the decimal point three places to the right.

So, the correct answer is:
**1,000**