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

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

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New post 02 Feb 2019, 20:31
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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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New post 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. \(x = \frac{(423-4)}{990} = = \frac{419}{990}\)

Answer: Option E
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Re: Express the value 0.4232323….. as a quotient of two numbers  [#permalink]

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New post 12 Feb 2019, 20:36
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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: \(0.232323.. = \frac{23}{99}\)

\(\frac{4}{10} + \frac{23}{990}\)

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

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