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# Convert decimal to fraction

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Manager
Joined: 10 Nov 2010
Posts: 246

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Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
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WE: Information Technology (Computer Software)

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31 Jan 2011, 21:25
Question:: Convert X=.262626.... into a fraction.

100x=26.2626....
100x-x=26
99x=26
x=26/99

Why x is subtracted from 100x?
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Re: Convert decimal to fraction [#permalink]

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31 Jan 2011, 21:31
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Expert's post
GMATD11 wrote:
Question:: Convert X=.262626.... into a fraction.

100x=26.2626....
100x-x=26
99x=26
x=26/99

Why x is subtracted from 100x?

To get rid of the infinite chain of 26s

x = .26262626....
100x = 26.26262626....
The right sides of the equations are the same. When we subtract, we get rid of .26262626.... and that is what we want if we want to convert a non terminating repeating decimal to a fraction. Else with infinite .26s, how many zeroes will you put in the denominator to convert it to a fraction (i.e. say 2.6 = 26/10, .2626 = 2626/10000, what about .26262626... infinite?)
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Joined: 21 Dec 2010
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Re: Convert decimal to fraction [#permalink]

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31 Jan 2011, 22:48
thats right for recurring decimals. thanks again.. any such techniques for non recurring decimals ?
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Re: Convert decimal to fraction [#permalink]

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01 Feb 2011, 03:17
GMATD11 wrote:
Question:: Convert X=.262626.... into a fraction.

100x=26.2626....
100x-x=26
99x=26
x=26/99

Why x is subtracted from 100x?

Converting decimals (terminating, recurring and mixed) to fractions: math-number-theory-88376.html (chapter "Converting Decimals to Fractions")
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Re: Convert decimal to fraction [#permalink]

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10 Jan 2014, 04:02
garimavyas wrote:
thats right for recurring decimals. thanks again.. any such techniques for non recurring decimals ?

I am rather late in answering this but still, let me point out that non-terminating non-repeating decimals (I am assuming that's what you meant) are irrational numbers. It means that they do not have an exact fraction representation.
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Re: Convert decimal to fraction   [#permalink] 10 Jan 2014, 04:02
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