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Convert decimal to fraction

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Convert decimal to fraction [#permalink] New post 31 Jan 2011, 20:25
Question:: Convert X=.262626.... into a fraction.
Answer ::

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] New post 31 Jan 2011, 20:31
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GMATD11 wrote:
Question:: Convert X=.262626.... into a fraction.
Answer ::

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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Re: Convert decimal to fraction [#permalink] New post 31 Jan 2011, 21:48
thats right for recurring decimals. thanks again.. any such techniques for non recurring decimals ?
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Re: Convert decimal to fraction [#permalink] New post 01 Feb 2011, 02:17
Expert's post
GMATD11 wrote:
Question:: Convert X=.262626.... into a fraction.
Answer ::

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] New post 10 Jan 2014, 03:02
Expert's post
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, 03:02
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