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If you had said that the 2s keep going indefinitely, or if you had just shown some dots ...

at the end of the number to suggest that they keep going, then the number would have been

equivalent to 2/9 .

But you gave no hint that what we see in the question is not complete, or that there's

any more to it than the twelve 2s we see. So we have to take it exactly as we see it.

The decimal that you posted, expressed as a fraction, is 222,222,222,222/1,000,000,000,000 .

When the fraction is reduced to lowest terms, it's 111,111,111,111/500,000,000,000 .

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Q: How do you write 0.222222222222 as a fraction?
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