To convert the repeating decimal 0.123123123... into a fraction, let's denote it by \( x \):
\[ x = 0.123123123\ldots \]
Notice that the repeating part "123" has a length of 3 digits. We can multiply \( x \) by 1000 (since "123" has three digits) to shift the decimal point three places to the right:
\[ 1000x = 123.123123123\ldots \]
Now, we can set up the equation by subtracting the original \( x \) from this new equation:
\[ 1000x - x = 123.123123123\ldots - 0.123123123\ldots \]
This simplifies to:
\[ 999x = 123 \]
Next, we solve for \( x \):
\[ x = \frac{123}{999} \]
Now, we can simplify the fraction \( \frac{123}{999} \) by finding the greatest common divisor (GCD) of 123 and 999, which is 3:
\[ \frac{123 \div 3}{999 \div 3} = \frac{41}{333} \]
Therefore, the repeating decimal \( 0.123123123\ldots \) can be expressed as the fraction \( \frac{41}{333} \).
None of the provided answer options match this, but from the calculations, we can confidently say that \( 0.123123123\ldots \) is a rational number. If you meant to ask for the closest or something specific, please clarify.
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