To convert 0.264¯¯¯¯¯¯¯¯

Question

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

Answer 1

To convert the repeating decimal \(0.264\overline{264}\) to a rational number, you need to multiply both sides of the equation by 1,000. This will shift the decimal point three places to the right, aligning the repeating part.

Here's the reasoning:

1. Set \(x = 0.264\overline{264}\).

2. Multiply both sides by 1,000:

   \[ 1,000x = 264.264\overline{264} \]

This allows you to eliminate the repeating decimal. Thus, the correct answer is:

1,000