How Do You Prove That 0.17 Reoccurring Is Equal To The Fraction 77/99?

2 Answers

Anonymous Profile
Anonymous answered
Take 0.1717...to be x
multiply by 100 on both sides
thus we have,
100x = 17.1717...
But we know that 0.1717 = x (Look at the 1st line)
Thus we have,
100x = 17 + x
100x - x = 17
99x = 17
x = 17/99'
It cannot be 77/99.
 
Oddman Profile
Oddman answered
The sum of the infinite geometric series
1 + a + a2 + a3 + a4 + ...
is given by
S = 1/(1-a)
where |a| < 1.

The series 1.010101010101 ... (infinitely repeating) has a=.01, so its value is 1/(1-.01) = 1/.99
This means .17171717... = .17*(1/.99) = .17/.99 = 17/99

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