Question

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

10
10

999
999

1,000

Answer 1

To convert \(0.264\overline{6}\) (where the 6 is the repeating part) to a rational number, you would set \( x = 0.264666...\).

To isolate the repeating part, you would multiply both sides of the equation by 10, because multiplying by 10 shifts the decimal point one place to the right. This gives:

\[
10x = 2.64666...
\]

Next, if you multiply by 1000, you will also involve all the digits to the right of 0.2646, which is 10 times the space utilized already:

\[
1000x = 264.666...
\]

The correct answer for isolating the repeating decimal part in this case is:

**1000**.