Question 900906: Hello, can someone please explain how or why the final answer is reduced
= 1346.8 = 6734/5,
F = 6734/(5*999) = 6734/4995 = 182/135
I am confused on this and was hoping someone could elaborate on this method of reduction..is it a property that has a name etc. Thanks
here is the whole problem example that I am studying.
F = 1.3481481481481...
1000 F = 1348.1481481481481...
999 F = 1346.8000000000000...
= 1346.8 = 6734/5,
F = 6734/(5*999) = 6734/4995 = 182/135
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You are being asked to show that F is a rational number.
It is rational because it is a repeating decimal form.
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How to work it::
F = 1.3481481481481...
Since the repeat starts after the 3, multiply by 10 to get:
10F = 13.481481...
Since the repeat extends to the thousands place, multiply by 1000 to get:
10,000F = 13481.481481...
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You have isolated the infinite repeating portion of F.
Subtract to get:
(10,000-10)F = 13481-13
9990F = 13468
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F = 13468/9990 (which mean F is rational)
You could reduce this to
F = 6734/4995
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Cheers,
Stan H.
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