Which of these nonterminating decimals can be converted into a rational number?

A. 0.626226222...
B. 0.020220222...
C. 0.123123123...
D. 0.898998999...

C?

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To determine which of the given nonterminating decimals can be converted into a rational number, we need to look for patterns or recurring digits in the decimal representation.

Let's analyze each option:

A. 0.626226222...
There does not seem to be a repetitive pattern or recurring digits in this decimal representation. It does not appear to be a rational number.

B. 0.020220222...
Once again, there is no clear pattern or recurring digits. It does not appear to be a rational number.

C. 0.123123123...
This decimal representation shows a repeating pattern of the digits 1, 2, and 3. The three digits repeat indefinitely. Thus, it can be converted into a rational number. The prefix "0." is followed by the repeating pattern "123."

D. 0.898998999...
Similar to option C, this decimal representation also exhibits a repeating pattern. The digits 8 and 9 repeat indefinitely. Hence, it can be converted into a rational number. The prefix "0." is followed by the repeating pattern "8989."

Therefore, the correct answer is C. 0.123123123...