### Here's a thought...

Prove that 1.0 and .9 (repeating) are **mathematically equal**

There are two ways to do this:
- We know that

1/9 = .1 (repeating)

2/9 = .2 (repeating)

3/9 = .3 (repeating)

...

8/9 = .8 (repeating)

so it stands to reason that 9/9 = .9 (repeating)

but we also know that 9/9 = 1.0

- Or if we simply add:

1/9 + 8/9 = 9/9

put another way...

.1 (repeating) + .8 (repeating) = .9 (repeating)

and we know that 9/9 = 1.0

so .9 (repeating) = 1.0