Let n = .234....
Now our job is to get the entire part that repeats on the left of the decimal point.
If we multiply the number by 1000 exactly one 2, one 3 and one 4 will move to the left.
So 1000n = 234.234... now lets remove our original number
- n = -.234... Notice how all the repeaters minus all the repeaters
999n = 234 leaves only the 234 that we move to the left of
the decimal point
Now lets divide both side by 999
999n = 234
999 999 this is the answer in unreduced form 9 can go into both = 26
111
Try it on your calculator (divide 26 by 111)
