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 $0.0012121212\dots$?
Why does $(10^4 - 10^2) \cdot 0.0012121212\dots = 12$?
0
$\begingroup$
arithmetic
exponentiation
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0How is $10^4-10^2=10^4$? – 2012-07-05
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0woops! good catch thanks. i meant 10^2 – 2012-07-05
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3It's not that either. $10000 - 100 = 9900$ – 2012-07-05
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1What is PEMDAS? – 2012-07-05
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0@Chris: GoogleIsYourFriend – 2012-07-05
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0@ChrisEagle: Parenthesis, Exponentiation, Multiplication, Division, Addition, Subtraction. The order of operations taught in some place. – 2012-07-05
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0http://www.wolframalpha.com/input/?i=%2810%5E4+-+10%5E2%29+%28.0012%29 – 2012-07-05
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1@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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0ye. so you first do the parenthesis yeilding 10^2 then you multiply by .0012 which should give you .12 not 12 – 2012-07-05
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0please realize that only the 12 is repeating not the two 00 in .0012 it doenst relally matter either way though – 2012-07-05
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0@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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1@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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0@Isaac: Oh well, I rather be well-educated. :-) – 2012-07-05
2 Answers
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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0oh woops I see the problem I was dividing therby subtracting the exponents. thanks! – 2012-07-05