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3 of 4 shorter solution

## GNU sed, 17 14 + 1(r flag) = 15 bytes

Edit: -2 bytes thanks to Riley

s:.*([^0]):\1:


It works by deleting everything until the right-most nonzero digit, which is then printed along with possible trailing zeros. The script can also handle multiple inputs, one per line.

Try it online! (all test examples)