Quite simply. Just take the repeating number and put it over 9, 99, 999, or whatever according to the amount of digets is has. For example, 0.666666666666666...... would be 6/9, and o.8989898989...... would be 89/99.
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All terminating decimals can be written as fractions.
Whole numbers are positive numbers and there are no fractions or decimals.
If you can completely write a number, using digits, fractions and decimals, then the number is rational. You appear to have accomplished that.
Decimals are fractions. Fractions are easy to picture graphically. Considering them in a concrete fashion makes the basic operations of addition and subtraction easy to visualize.
If you can completely write a number, using digits, fractions and decimals, then the number is rational. You appear to have accomplished that.