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# Which of the following is closest to \frac{1}{9} +

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Manager
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Which of the following is closest to \frac{1}{9} + [#permalink]

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02 Aug 2008, 20:37
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Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5
Director
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02 Aug 2008, 20:42
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Manager
Joined: 22 May 2007
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02 Aug 2008, 20:45
durgesh79 wrote:
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Durgesh,

How does one solve this quickly ? Did you calculate each fraction? IS there a way to quickly do this?
Director
Joined: 27 May 2008
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02 Aug 2008, 20:49
aaron22197 wrote:
durgesh79 wrote:
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Durgesh,

How does one solve this quickly ? Did you calculate each fraction? IS there a way to quickly do this?

my experiance in comparing fraction says .... do one of two things
covert everything to common denominator
OR
covert everything to decimals

in this case converting to common denominator is tough ... and these fractions are simple ones ... we know 1/10 and 1/9
all you need todo is convert 1/99, 1/999 and 1/8 .... option D and E are already eliminated ....
VP
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02 Aug 2008, 20:54
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Closest options for the above question are :
(A) and (B)

now say x=$$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$
x-1/9=$$\frac{1}{99} + \frac{1}{999}$$
x-1/10 = $$\frac{1}{90} + \frac{1}{99} + \frac{1}{999}$$

hence x-1/10 > x-1/9 => 1/9 is closest
good question
_________________

cheers
Its Now Or Never

Manager
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03 Aug 2008, 01:14
Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Re: 1/999   [#permalink] 03 Aug 2008, 01:14
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