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# If 100/3=x then why does x*3 not equal 100?

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If 100/3=x then why does x*3 not equal 100?

If you divide 100 by 3 you get 33.33333333 etc. And if you times that number by 3 you get 99.9999999 etc. Why do you not get 100?

Guest Jun 6, 2017
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$$99.\overline{9999}=100$$ This statement to my left is actually true. Let's prove that by manipulating the number:

 $$99.\overline{9999}=x$$ I'll set it equal to some number. Multiply both sides by 10 $$999.\overline{9999}=10x$$ This might be the hardest step to understand. Subtract x on both sides! $$999.\overline{9999}-99.\overline{9999}=10x-x$$ Simplify both sides of the equation $$900=9x$$ Divide by 9 on both sides $$100=x$$

WOAH! $$99.\overline{9999}=100$$. It's kind of disguised, isn't it?

TheXSquaredFactor  Jun 6, 2017

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