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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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16 Jan 2019, 02:09
00:00

Difficulty:

35% (medium)

Question Stats:

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

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GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5042
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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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

Manager
Joined: 01 May 2017
Posts: 82
Location: India
What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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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.

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Joined: 24 Dec 2011
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Location: India
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WE: General Management (Health Care)
Re: What is the value of (1 - 10^{-3})(0.270270270270....), where .....  [#permalink]

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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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