Example: Suppose x = 0.0909090909...... etc
Then 100x = 9.0909090909..... etc.
Subtract x from 100x to get 99x = 9
Divide by 99 and simplify: x = 9/99 or x = 1/11
x is therefore the ratio of two whole numbers (1 and 11) and is, by definition, rational.
