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FDP Problem (OG PS #174)

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FDP Problem (OG PS #174)

by mattnyc15 » Fri Jan 15, 2016 10:13 am
PS #174 OG 2016

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely.
What is the value of (10^4 - 10^2)(0.0012)

Note: 12 has bar above.

A. 0
B. 0.12
C. 1.2
D. 10
E. 12

[spoiler]OA: 12[/spoiler]


I'm very confused. Here I followed PEMDAS and did the following:

(10^4 - 10^2) = (10^2)
(10^2)(.0012) = .12, Answer B.

Why am I suppose to distribute .0012 to 10^4 and 10^2?
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by [email protected] » Fri Jan 15, 2016 10:29 am
Hi mattnyc15,

I'm going to point out an error that you made so that you can reattempt this question:

10^4 = 10,000
10^2 = 100

10^4 - 10^2 is NOT 10^2

If you do that subtraction correctly, you can then take advantage of how the answer choices are 'spread out' and actually estimate the correct answer.

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Rich
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by ceilidh.erickson » Fri Jan 15, 2016 10:30 am
Be careful! You can't simply subtract the exponents when you're subtracting 10^4 - 10^2. Those actual numbers would be 10,000 - 100, which would yield 9,900, not 100.

If you simplified to 9,900, though, you'd still have trouble coming up with an answer. You would be multiplying an integer by a non-terminating decimal, so the answer would go on forever!

Look at the answer choices: they're (almost) all relatively simple, terminating answers. That's our clue that there's a simpler way of solving than doing long multiplication. Since 10^4 and 10^2 are powers of 10, that should trigger us to this about DECIMAL PLACEMENT.

If we distribute, the 10^4 shifts the decimal 4 places, and the 10^2 shifts the decimal 2 places:
12.12 - 0.12 (assume the bars are above and not below)

Since both contain the 0.12, when we subtract we get rid of the decimal entirely, and are left with 12.
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by ceilidh.erickson » Fri Jan 15, 2016 10:31 am
Jinx! Rich and I posted the same thing at almost exactly the same moment. Great minds...
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