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Originally Posted by worldbringer
.333333 is not a perfect representation of 1/3. .9999999 is not a perfect representation of 1.
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However,
.333... is a perfect decimal representation of 1/3 ( which equals 3/9), and
.999... is a perfect decimal representation of 1 (which equals 9/9). Those three trailing dots ("ellipses") are there for a reason, and that reason is why repeating decimals can be used to represent any rational number.