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# Classic puzzle: .9999..... AND 1

### #11

Posted 05 November 2013 - 10:26 PM

well, not entirely sure i agree. for example, how would you denote 1/13?

you need a consistent way of denoting any rational number, not just ones that repeat the last digit.

personally, i like the bar method, where the repeated values have a bar over the top over the length of the repeating part.

so

_ 0.9 = 1would be more accurate (although more cumbersome.)

______

1/13 = 0.076923

The bar covers the part that repeats.

here's my challenge for you.

accurately add 1/13 to 45/89 in decimal representation.

This can be done, but would be rather tedious (particularly as the decimal expansion for 45/89 has a relatively long repeating digit string). The sum will also have a repeating pattern, of some size less than or equal to the LCM of the repeating digit string lengths of the two operands.

### #12

Posted 05 November 2013 - 11:45 PM

well, not entirely sure i agree. for example, how would you denote 1/13?

you need a consistent way of denoting any rational number, not just ones that repeat the last digit.

personally, i like the bar method, where the repeated values have a bar over the top over the length of the repeating part.

so

_ 0.9 = 1would be more accurate (although more cumbersome.)

I might have missed the gist of this question the first time around...

Another way to express 1/13 is 0.076923076923076923...

It is clumsy compared with the bar method in this example (unlike .999...), but still understandable.

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