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

Question

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