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let x = 0.125r
1000x = 125.125r
(Subtract x from both sides, we have defined x as 0.125r. 125.125r - 0.125r must = 125)
999x = 125
x = 125/999
I assure you that's correct.
Using the same maths:
x = 0.9r
10x = 9.9r
9x = 9
x = 9/9
x = 1
Or think about it this way. If two numbers are different, you prove this by subtracting them, and getting a difference. 0.9r continues into infinity, therefore there is no difference between 0.9r and 1, therefore 0.9r = 1.
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