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When you answer this question $(10^4 - 10^2) \cdot 0.0012121212\dots$ you get $12$. However, that seems to defy PEMDAS. Please explain. Doing PEMDAS wouldn't you get $(10^4 - 10^2)$ = $10^2$ and then multiply that by $0.0012121212\dots$?

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    How is $10^4-10^2=10^4$?2012-07-05
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    woops! good catch thanks. i meant 10^22012-07-05
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    It's not that either. $10000 - 100 = 9900$2012-07-05
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    What is PEMDAS?2012-07-05
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    @Chris: GoogleIsYourFriend2012-07-05
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    @ChrisEagle: Parenthesis, Exponentiation, Multiplication, Division, Addition, Subtraction. The order of operations taught in some place.2012-07-05
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    http://www.wolframalpha.com/input/?i=%2810%5E4+-+10%5E2%29+%28.0012%292012-07-05
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    @AsafKaragila: except that it really should be: Parentheses, Exponentiation, Multiplication and Division, Addition and Subtraction (and many students mislearn order of operations because of PEMDAS).2012-07-05
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    ye. so you first do the parenthesis yeilding 10^2 then you multiply by .0012 which should give you .12 not 122012-07-05
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    please realize that only the 12 is repeating not the two 00 in .0012 it doenst relally matter either way though2012-07-05
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    @Isaac: I don't recall any such laws, nor I was taught any during my undergrad or otherwise. I was bound to get it wrong! :-)2012-07-05
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    @AsafKaragila: It's very hard to keep track of bad/wrong mnemonic devices when one didn't learn them and instead learned the correct concept. :)2012-07-05
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    @Isaac: Oh well, I rather be well-educated. :-)2012-07-05

2 Answers 2

5

I figure it might be easier to see like this.

$10^4\times0.001212...=12.1212..$

$10^2\times0.001212...=0.1212...$

Now subtract.

$(10^4\times0.001212...)-(10^2\times0.001212...)=12$

Using the distributive property, we can rewrite this as

$(10^4-10^2)\times0.001212...=12$

3

First, let $n=0.0012121212\dots$ so that $100n=0.12121212\dots$. Subtracting, $100n-n=99n=0.12=\frac{12}{100}$, so $n=\frac{12}{9900}$ (I'm intentionally not simplifying those fractions).

Now, as pointed out in the comments, $10^4-10^2=10000-100=9900$, so $$(10^4-10^2)(0.0012121212\dots)=9900\cdot\frac{12}{9900}=12.$$

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    oh woops I see the problem I was dividing therby subtracting the exponents. thanks!2012-07-05