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# Express the repeating decimal .1405405405405405.... as a

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Manager
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Express the repeating decimal .1405405405405405.... as a [#permalink]

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24 Feb 2005, 18:35
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Express the repeating decimal .1405405405405405.... as a fraction in lowest terms.
Manager
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25 Feb 2005, 12:31
Well it is part of arithmetic. GMAT doesn't have a rigid syllabus for quant, does it?
Senior Manager
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26 Feb 2005, 12:18
typical backsolving question
not really concerning
VP
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26 Feb 2005, 23:28
anirban16 wrote:
Express the repeating decimal .1405405405405405.... as a fraction in lowest terms.

OOOOOOOOOOHHHHHHHHHHHHHHHHHHHHHHHHHHH,

=26/185
Manager
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27 Feb 2005, 01:17
I agree with thearch.It is definately backsolvable question.However I would love to know if there is any easy method to solve it.
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28 Feb 2005, 15:05
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Well the trick here is that any repeating decimal can be represented as a fraction by taking the Nr as the repeated part and the Dr as the number of 9s as the number of digits that gets repeated.

So say for instance .4545454545.... = 45/99

.405405405.......... = 405/999

So in our case we have .1405405405...

So multiply by 10 and divide by 10.

So we have 1.405405405.../10 = (1 + .405405405405)/10

= (1 + 405/999)/10 = (1+15/37)/10 = 52/(10*37) = 26/185
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28 Feb 2005, 17:32
Great !!! Now that I know the trick, I wish I get a question in the test on this.
Director
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28 Feb 2005, 18:01
Looks like i just saw magic...WOW! But what are the odds of seeing this on the test?
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Easier way to solve this! [#permalink]

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01 Mar 2005, 03:51
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0.1405405405 can be written in fractional form as (1405-1)/9990.

Other examples can be 0.121212121=(121-1)/990

In short, for denominator: place as much nine as repeating number followed by same number of zero as non repeated number.

in numerator: difference between all number formed by all the decimal digit and non repeatative digits.

Hope this help!

Shishir
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01 Mar 2005, 10:52
is there any fast way to find the equivalent for : 405/999?

as 15/37?
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01 Mar 2005, 11:53
You know that both Nr and Dr are divisible by 9 (as the sum of the digits in each number is divisble by 9).Now you will get 45/111 now again you know this is divisble by 3.

Anybody knows a good link to a site explaining these division rules.
VP
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01 Mar 2005, 22:33
MA wrote:
anirban16 wrote:
Express the repeating decimal .1405405405405405.... as a fraction in lowest terms.

=26/185

Alright guys, here is the process:
suppose x=.1405405405405405, which is actually is not a repeating decimal. lets make it as repeting decimal by multiplying 10 (because with this multiplication 1 comes before the decimal and remaining decimal will be the repeating decimal) as under:
(i) 10x=1.405405405405
(ii) multiply this eq by 10^3 (because there are 3 repeating numbers: 4, 0, and 5) => 1,000(10x)=1405.405405405405405405405405405405
(iii) now, substract 10x from both side (because we are eliminating the decimal)

9,990x=1405.405405405-1.405405405

x=1404/9990=26/185

i believe, this method can be applied in any fractions. for example
x=0.2222222222222222222222222222222
(i) x=0.222222222222222
(ii) 10x= 2.2222222222222222
(iii) 9x=2
x =2/9
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02 Mar 2005, 18:47
700Plus wrote:
You know that both Nr and Dr are divisible by 9 (as the sum of the digits in each number is divisble by 9).Now you will get 45/111 now again you know this is divisble by 3.

thank you 700Plus for the tip!!, now I remember reading this on the Kaplan Math workbook....

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Manager
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04 Mar 2005, 13:18
Yup that's how to treat repeating decimals. Multiply by 10s to get the repeating part and then subtract. That's the logic behind the 9s.
Director
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08 Jul 2007, 16:57
What about other #s? For example 3/11? There are 2 digits repeating, but they are 2 & 7 not 3. Thoughts?
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Re: Express the repeating decimal .1405405405405405.... as a [#permalink]

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22 Dec 2014, 11:02
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Re: Express the repeating decimal .1405405405405405.... as a   [#permalink] 22 Dec 2014, 11:02
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