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## anonymous one year ago Is 3/3 actually 1? Because she I add 33.3333%+33.3333%+33.3333%. You get 99.9999%.

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1. jjuden

3/3 is 1 cause its a fraction

2. geerky42

1/3 is NOT 33.3333% It is 33.3333333333333333333333333.... and so on forever

3. anonymous

Well, $\frac{ 1 }{ 3 }$ is a repeating decimal. So 33.3333% is an approximation.

4. anonymous

Ya but wouldn't the sum be 99.9999999repeating and never reach 100?

5. anonymous

You raised a good point though since computer systems have to store repeating decimals as approximations in the form of a mantissa floating point, as per IEEE 754.

6. anonymous

Ok cool, thanks.

7. geerky42

There is argument that $$99.9999999999999999999999...\% = 100\%$$ Or at least more commonly, $$0.999999999999... = 1$$

8. geerky42

Well technically it IS 100%. Because otherwise THERE will be exists another value between 99.9999...% and 100%. What is this value? Not that I know of.

9. anonymous

Ok cool thanks. :)

10. geerky42

No problem.

11. freckles

$x=.999999999999999999.... \\10x=9.99999999999999999999999........... \\ 10x-x=9 \\ 9x=9 \\ x=1$

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