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I don't think that would be true seeing 1/3 = 0.3333.. , or am I reading this wrong?

3 recurring represents a particular quantity continuing forever.

0 recurring represents the end of a quantity, and the absence of any further quantity, forever.

Eg: 0.012500000000000...

The significant portion is 0.0125 - the recurring zeroes serve a mathematical role akin to that of a full-stop in a sentence. Hence zero being (jokingly, but in a sense truthfully) always the "last digit".

This is just an artifact of representing it in base-10. In base-3 0.0125 has the same value but would have a non-terminating representation of 0.00010001...

I will grant that in base-π, π is 10, however.

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