Recurring decimal to fraction?

How do you write 0.9999 recurring as a fraction. I know how to do ones like:

0.8dot(8)=8/9 and so on. using 1/9 1/99 1/90 etc. The problem is you can't do it with 9 repeating.

1 Answer
Jun 8, 2018

0.bar9=1

0.bar8 = 8/9

Explanation:

let:

m=0.bar9

10m=9.bar9

subtract the first equation from the second one:

10m=9.bar9
underline("- "m=0.bar9)
" "9m=9

m=1

The other problem:

let:

m=0.bar8

10m=8.bar8

subtract the first equation from the second one:

10m=8.bar8
underline("- "m=0.bar8)
" "9m=8

m=8/9