Jack, the notation 0.333... is a mathematical shortcut for writing in decimal a fraction that has an infinite number of decimal places. You read it as, "point 3, 3, 3 repeating forever". If you continue to work with fractions, it's quite clear that:

1/3 * 3 = 1

This is read as "one third times three equals one." It is not as obvious in decimal, but it's still true that:

.333... * 3.0 = 1.0

Reading, "point 3, 3, 3, repeating forever times three point zero equals one point zero". It's just hard to wrap your head around an infinitely repeating decimal.

EDIT: proof of this is left to the reader. Also, check your calculator because it knows the answer as well.

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Posted 5 years ago