What is the rational fraction represented by this decimal expansion: 0.48031496062992125984251968503937.......etc? Thanks for help.
+33616 What do you mean by "....etc"? I see no repetition (which there needs to be if the number is rational).
I believe it has a period of more than 32 digits long, which is the maximum display of my calculator.
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
