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

123/1000

12 13/10

1 23/100

123/999

Answer 1

To convert the repeating decimal \(0.123123123...\) into a fraction, we can follow these steps:

1. Let \(x = 0.123123123...\).
2. Since the decimal repeats every three digits, we can multiply \(x\) by 1000 to shift the decimal point three places to the right:
\[
1000x = 123.123123123...
\]
3. Now we have two equations:
\[
x = 0.123123123...
\]
\[
1000x = 123.123123123...
\]
4. Subtract the first equation from the second:
\[
1000x - x = 123.123123123... - 0.123123123...
\]
\[
999x = 123
\]
5. Now, solve for \(x\):
\[
x = \frac{123}{999}
\]
6. Now, we can simplify \( \frac{123}{999} \):
\[
\frac{123 \div 123}{999 \div 123} = \frac{1}{9}
\]

Hence, in its simplest form, the answer is \( \frac{123}{999} \).

So the answer is:

**123/999**