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What is the value of (1 - 10^{-3})(0.270270270270....), where .....

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What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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New post 16 Jan 2019, 02:09
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:31) correct 32% (02:07) wrong based on 71 sessions

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Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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New post 16 Jan 2019, 02:30
given expression can be written as:
(1-10^-3) * ( 0.270)
(0.999) * (0.270)
0.99 ~ 1
1* 0.270
= 0.27
IMO B




EgmatQuantExpert wrote:
What is the value of \((1 - 10^{-3})(0.270270270270....)\)?

    A. 0.027
    B. 0.27
    C. 2.7
    D. 27
    E. 270

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What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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New post 16 Jan 2019, 02:39
What is the value of \((1−10^−3)(0.270270270270....)\)

By rounding of rule \(27/999 = 0.0270270...\)
27*10/999 = 0.270270..
implies \((1-10^-3)(27/999) = (999/1000)*(27*10/1000) = 27*10/1000\)
= 0.27

Option B is correct
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Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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New post 18 Jan 2019, 01:36

Solution


Given:
    • An expression, (1 - 10^{-3})(0.270270270…)

To find:
    • The value of (1 - 10^{-3})(0.270270270…)

Approach and Working:
    • \((1 - 10^{-3})(0.270270270…) = (1 – \frac{1}{10^3})(\frac{270}{999}) = \frac{(10^3 – 1)}{10^3} * \frac{270}{999} = \frac{999 * 270}{10^3 * 999} = \frac{270}{1000} = 0.27\)

Hence the correct answer is Option B.

Answer: B

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Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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New post 15 May 2019, 09:39
reducing the recurring decimal
x=0.270270270------(1)
1000x=270.270270-------(2)

(2)-(1)-----
999x=270
x=270/999

(1-10^-3)
(999/1000) * (270/999)

270/1000=0.27
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Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....   [#permalink] 15 May 2019, 09:39
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