Question

Change the decimal to a fraction: 0.123123123….(1 point)
Responses

This decimal is Irrational and cannot be written as a fraction
This decimal is Irrational and cannot be written as a fraction

121310

12 and 13 tenths

1231000

123 over 1000

123100

1 and 23 over 100

123999

Answer 1

0.123123123... = 0.\overline{123}. Let x = 0.\overline{123}. Then 1000x = 123.\overline{123}, so 1000x − x = 123 ⇒ 999x = 123 ⇒ x = 123/999 = 41/333.

So the fraction is 41/333 (equivalently 123/999).