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 1,000 1,000 999 999 10 10 100 100

Answer 1

To convert the repeating decimal \(0.264\overline{264}\) to a rational number, you would set \(x = 0.264\overline{264}\) and then multiply both sides of the equation by \(1,000\) (since the repeating part "264" has 3 digits).

Here's how it works:

1. Let \(x = 0.264264264...\)
2. Multiply both sides by \(1,000\): \[ 1000x = 264.264264264... \]
3. Now, you can subtract the original equation from this new equation to eliminate the repeating part.

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