n repeating digit of decimal number

I have a problem how to convert number 0.3333....3 where 3 repeats N times to fraction.

for N=1 0.3

N=2 0.33 and so on.

I know how to convert number where digits repeats forever, but how can I convert this to fraction to get correct result for any N.

Thanks in advance

Re: n repeating digit of decimal number

Quote:

Originally Posted by

**Bokas** I have a problem how to convert number 0.3333....3 where 3 repeats N times to fraction.

for N=1 0.3

N=2 0.33 and so on.

I know how to convert number where digits repeats forever, but how can I convert this to fraction to get correct result for any N.

Thanks in advance

Re: n repeating digit of decimal number

Quote:

Originally Posted by

**Bokas** I have a problem how to convert number 0.3333....3 where 3 repeats N times to fraction.

for N=1 0.3

N=2 0.33 and so on.

I know how to convert number where digits repeats forever, but how can I convert this to fraction to get correct result for any N.

Thanks in advance

A terminating decimal is **easier** than a repeating decimal (which is what ProveIt did). If x= 0.33333..3 where the "3" repeats N times, then so that . Because of that " " in the denominator, a terminating decimal, converted to a fraction, has only powers of 2 and 5 in its denominator.

Re: n repeating digit of decimal number