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Convert Recurring Decimal into Fraction

I saw this on the Toolkit's questions and thought it would be good that everyone knows this.

To convert a recurring decimal to fraction: (Example to be used: 0.84027840278402784027)
1. Separate the recurring number from the decimal fraction (i.e. from the number above this step will produce 84027) - This number is now going to be the numerator
2. Count the number of digits in the number (In this case it will be 5)
3. In the denominator write down 9 the same number of times as the number found in step 3 (i.e. 9 to be write five times making the denominator 99999)

Thus the fraction is now the numerator from step 1 and the denominator from step 3 (i.e. 0.840278402784027840278402784027 = 84027/99999)

Try this with any recurring number. I am not too sure but I think the properties being used here are the ones of numbers 9 and 11. Please confirm if this assumption is correct.
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One thing that I learned, more like stumbled upon, while preparing was that if you are to square any number, the just multiple the number before and after that number, and then add 1.

i.e. \((n-1)*(n+1) + 1 = n^2\)


Also, think about why it is so.

\((n-1)*(n+1) = (n^2 - n + n - 1) = n^2 - 1\)

Therefore, \((n-1)*(n+1) + 1 = n^2 - 1 + 1 = n^2\)
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RnH
One thing that I learned, more like stumbled upon, while preparing was that if you are to square any number, the just multiple the number before and after that number, and then add 1.

i.e. \((n-1)*(n+1) + 1 = n^2\)


Also, think about why it is so.

\((n-1)*(n+1) = (n^2 - n + n - 1) = n^2 - 1\)

Therefore, \((n-1)*(n+1) + 1 = n^2 - 1 + 1 = n^2\)

Exactly! I had problems with higher multiples of 7 and this helped me get over the issue.
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Can anyone explain the significance of the grouping of numbers on the first page of the "what to remember" PDF file? it goes from 14-240? Is the file incomplete or am I missing something? Was something cut off? Thanks
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Can anyone explain the significance of the grouping of numbers on the first page of the "what to remember" PDF file? it goes from 14-240? Is the file incomplete or am I missing something? Was something cut off? Thanks

Hi,
Those are the tables of the numbers that head the column i.e 14, 16, 17,... 24.

Hope this helps!!!
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Why does the file say 69 is prime?
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Nice info, thanks!
Is this much sufficient or is Vedic Mathematica book useful for gmat?

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