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

1,000
1,000

999
999

100
100

10

Answer 1

1000

Since the repeating block "264" has 3 digits, multiply by 10^3 = 1000:
x = 0.\overline{264} → 1000x = 264.\overline{264}, then subtract to get 999x = 264.