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

123999
123
999

123 over 999

121310
12
13
10

12 and 13 tenths

123100
1
23
100

1 and 23 over 100

1231000

Answer 1

Let x = 0.\overline{123}. Then 1000x = 123.\overline{123}. Subtract: 1000x − x = 123 ⇒ 999x = 123 ⇒ x = 123/999. Simplify by 3: x = 41/333.

So 0.123123123... = 41/333 (equivalently 123/999).