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

10
10

100
100

999
999

1,000

Answer 1

To convert \( x = 0.264\overline{6} \) to a rational number, we need to eliminate the repeating decimal.

In this case, the repeating part is "6," which has one digit. Therefore, we multiply both sides of the equation by \( 10 \) to shift the decimal point one place to the right:

\[ 10x = 2.646666...\]

Thus, the correct answer is:

10