Thread: 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

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

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.

Thank you both