Originally Posted by Deanstar
Do you ever write a decimal number that goes on forever? Does any calculator?
Yes. We have a specifc way to do it. You use an ellipsis: 0.555... is different from 0.555.
I know you know the answer, so I'll tell you why infinity makes a difference here. If you refuse to use the decimal that goes on forever, you cannot write a third:
0.3 times 3 is 0.9, so it isn't 1 / 3.
0.333 times 3 is 0.999, so it isn't 1 / 3.
0.333333333333 times 3 is 0.999999999999, so it isn't 1 / 3.
But 0.333... times 3 is 1, making exactly one third.
If you want 1 / 3 you're going to need infinitely repeating decimals or you don't have a third.
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