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# Rational Fraction

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What is the rational fraction represented by this decimal expansion: 0.48031496062992125984251968503937.......etc? Thanks for help.

Nov 18, 2020

#1
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What do you mean by "....etc"?  I see no repetition (which there needs to be if the number is rational).

Nov 18, 2020
#2
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I believe it has a period of more than 32 digits long, which is the maximum display of my calculator.

Nov 18, 2020
#3
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61/127    according to Web2.0 calculator....

Nov 18, 2020
#4
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Use "continued fraction" method to determine relatively quickly if it is rational or irrational.

0.48031496062992125984251968503937
Take its reciprocal

2.0819672131147540983606557377049
Subtract 2, and take reciprocal of the fraction

12.2
subtract 12 and take reciprocal of 0.2

5. It terminates in 5.

Reverse the process by multiplying from the bottom up: 5 x 12.2 = 61 - this is the numerator.
61 x 2.0819672131147540983606557377049=127 - this is the denominator.

So, the fraction is: 61 / 127

Nov 18, 2020