why is every repeating decimal a fraction of 9?

No.14347490 ViewReplyOriginalReport
for any given simple repeating decimal (meaning the decimal place only has the repeating pattern) you can write any repeating decimal as

(repeating digits) / (number of digits in 9s)

example, 0.12345 = 12345 / 99999

what's so special about 9 as a denominator?