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# Express the value 0.4232323….. as a quotient of two numbers

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Manager
Joined: 11 Dec 2013
Posts: 114
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Express the value 0.4232323….. as a quotient of two numbers  [#permalink]

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02 Feb 2019, 20:31
1
3
00:00

Difficulty:

75% (hard)

Question Stats:

39% (01:30) correct 61% (01:07) wrong based on 54 sessions

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Find the value $$0.4232323…$$.. as a quotient of two numbers
A) $$\frac{423}{990}$$
B) $$\frac{423}{1000}$$
C) $$\frac{423}{999}$$
D) $$\frac{419}{999}$$
E) $$\frac{419}{990}$$

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Express the value 0.4232323….. as a quotient of two numbers  [#permalink]

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02 Feb 2019, 23:09
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4d wrote:
Find the value $$0.4232323…$$.. as a quotient of two numbers
A) $$\frac{423}{990}$$
B) $$\frac{423}{1000}$$
C) $$\frac{423}{999}$$
D) $$\frac{419}{999}$$
E) $$\frac{419}{990}$$

Let, $$x = 0.4232323…$$

i.e. $$10x = 4 +0.232323…$$

Let, $$a = 0.232323...$$
i.e. $$100a = 23+0.232323...$$
i.e. $$100a = 23+a$$
i.e. $$99a = 23$$
i.e. $$a = \frac{23}{99}$$

i.e. $$10x = 4 +\frac{23}{99}$$

i.e. $$x = \frac{(423-4)}{990} = = \frac{419}{990}$$

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##### General Discussion
Manager
Joined: 22 Sep 2018
Posts: 247
Re: Express the value 0.4232323….. as a quotient of two numbers  [#permalink]

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12 Feb 2019, 20:36
1
1
4d wrote:
Find the value $$0.4232323…$$.. as a quotient of two numbers
A) $$\frac{423}{990}$$
B) $$\frac{423}{1000}$$
C) $$\frac{423}{999}$$
D) $$\frac{419}{999}$$
E) $$\frac{419}{990}$$

My reasoning:

$$0.4232323... = (4.23232323...) * 10^{-1}$$

Continuing on:

$$(4 + 0.23232323) * 10^{-1}$$

A prime number divided by 9 is that number repeating hence: $$0.232323.. = \frac{23}{99}$$

$$\frac{4}{10} + \frac{23}{990}$$

= $$\frac{419}{990}$$
Re: Express the value 0.4232323….. as a quotient of two numbers   [#permalink] 12 Feb 2019, 20:36
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