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705-805 (Hard)|   Arithmetic|   Sequences|      
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4d
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GMAT 1: 730 Q51 V37
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Express the value 0.4232323….. as a quotient of two numbers 02 Feb 2019, 21:31
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E
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Difficulty:

75% (hard)

Question Stats:

48% (01:31) correct 52% (01:19) wrong based on 422 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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E
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Schools: IIM (A) ISB '24
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Express the value 0.4232323….. as a quotient of two numbers 03 Feb 2019, 00:09
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4d
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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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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NinetyFour
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Express the value 0.4232323….. as a quotient of two numbers 12 Feb 2019, 21:36
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4d
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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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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Express the value 0.4232323….. as a quotient of two numbers 19 Jan 2022, 15:28
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I had this question wrong but I now know how to solve it:

Find the value 0.4232323 as a quotient of two numbers

You should know, that when dividing a number (smaller than 9) by 9 or 99 or 999... the number will repeat itself after the comma of the decimal:

\(\frac{1}{9}\) = 0.1111111...
\(\frac{78}{99}\) = 0.78787878...

This way, we know that (C) \(\frac{423}{999}\) = 0.423423423...

However, we are looking for the fraction that gives us 0.423232323...

--> Cross out (C).

We also know that (B) \(\frac{423 }{ 1000}\) = 0.423

--> Cross out (B).

Look at (D): It will give us \(\frac{419}{999\\
}\) = 0.419419419...

--> Cross out (D).


We are now left with (A) and (E).

Since we are looking for a number that is between (D) = 0.419419419 and (C) = 0.423423423, the only option is

(E) \(\frac{419}{990}\)

because (A) \(\frac{423}{990}\) > 0.423423423...


Hope it helps! :)
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Express the value 0.4232323….. as a quotient of two numbers 23 Dec 2024, 10:56
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Set X = .42323...

So 10X = 4.2323.... and

X/10= .042323...

Therefore:

10X - X/10 = 4.19 or

100X - X = 99X = 41.9

Therefore X = 41.9/99 =

419/990
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Express the value 0.4232323….. as a quotient of two numbers 08 Jul 2026, 08:05
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