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A bar over a sequence of digits in a decimal indicates that

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Re: A bar over a sequence of digits in a decimal indicates that  [#permalink]

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New post 25 Apr 2019, 19:29
(10^4-10^2) * (0.0012)

(10^2-1)10^2 * (0.0012)

(100-1) * 0.12)

99 * 12/99

12
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Re: A bar over a sequence of digits in a decimal indicates that  [#permalink]

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New post 17 Oct 2019, 08:07
Approximation:

(10000-100)x(0.0012)=9900 x 0.0012 =99 x 0.12=100x 0.12= 12
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Re: A bar over a sequence of digits in a decimal indicates that  [#permalink]

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New post 09 Nov 2019, 11:57
This is a fairly easy question.
First, factor out 10^2:

10^2(10^2-1)(.0012)

100(100-1)*(.0012)

Consider the second parentheses to be ~100.

100*100=10^4*.0012.

Move decimal over 4 places and you arrive at 12.
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Re: A bar over a sequence of digits in a decimal indicates that  [#permalink]

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New post 17 Nov 2019, 06:29
Okay, so:

Take 15 seconds to read, take your notes, then:

(10^4-10^2)=(10000-100)
(0.0012) --> take 2 negative powers of 10 to take out 12; then, push it by 3 extra negative powers of 10: 2+3=5 so 0.0012=12 x 10^-5).

You approximate and get (10^4)x(10^1 x 10^-5) = everything is canceled out, only the 12 still exists: Answer E.

A problem that's easily ID-able and solvable in less than 50 seconds! :)
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Re: A bar over a sequence of digits in a decimal indicates that  [#permalink]

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New post 17 Nov 2019, 07:12
fatihaysu wrote:
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of \((10^4 -10^2)(0.00\overline{12})\)?

(A) 0
(B) 0.12
(C) 1.2
(D) 10
(E) 12

Anyway My approach is;

9900*12/9999 = 11,88 so i chose E

is there anyway ? i did right but dont know the logic under it


Expression = (100^2 - 10^2)*.0012*100/99 = 110*90*.0012*100/99= 9900*.12/99 = 12

IMO E

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Re: A bar over a sequence of digits in a decimal indicates that   [#permalink] 17 Nov 2019, 07:12

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