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I'm embarrassed to ask this fundamental question among questions of particle filters but : my daughter just had this marked wrong on a test.

The teacher said the answer was 1/3 of 240 = 80.

On one level I understand this using fractions (80 * 3 = 240) -- and at another level, typing this into a calculator (since we don't have infinite numbers) yields 79.9999999992. Doing this using fractional math makes sense but that's only because 240 "cleanly" has 3 pieces -- but how does this work decimally when we can't have infinite numbers and have to round up (which to me seems more an approximation than 79.992)

Why is my daughter's answer wrong? Can't they both be correct at different levels of precision? Is one answer fundamentally the correct one and why?

I hope I have the gist of my question down and thanks in advance for your answers.

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    Forgot to mention: Wolframalpha says it's 80 http://www.wolframalpha.com/input/?i=33+1%2F3%25+of+2402011-06-14
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    The moral is - don't use a calculator unless you have to.2011-06-14
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    I'm not sure what you mean by "we don't have infinite numbers" and "we can't have infinite numbers". The only way to represent the number $1/3$ exactly using decimal digits is $0.333333\dots$, with an infinite number of $3$s. This doesn't mean that the number $1/3$ is somehow more suspect or has less of an existence than $1/2$ or $1/5$; it just means that the decimal representation is not the best way to represent this number. And if you do not correctly do arithmetic on infinite strings of digits (which is sometimes possible, BTW, as it is here), then you will get a wrong answer.2011-06-14
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    Besides, in base 3, 1/3 doesn't repeat. It's $0.1$. Just do all your divisions by 3 in base 3: it's easier!2011-06-14

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