SOLUTION: F = 1.3481481481481... 1000 F = 1348.1481481481481... 999 F = 1346.8000000000000... = 1346.8 = 6734/5, F = 6734/(5*999) = 6734/4995 = 182/135 Hello, the above was an example

Algebra ->  Decimal-numbers -> SOLUTION: F = 1.3481481481481... 1000 F = 1348.1481481481481... 999 F = 1346.8000000000000... = 1346.8 = 6734/5, F = 6734/(5*999) = 6734/4995 = 182/135 Hello, the above was an example      Log On


   

Question 901051: F = 1.3481481481481...
1000 F = 1348.1481481481481...
999 F = 1346.8000000000000...
= 1346.8 = 6734/5,
F = 6734/(5*999) = 6734/4995 = 182/135
Hello, the above was an example I was studying, an example of how to convert a repeating decimal into a fraction. I understand it! I understand reducing the answer using primes etc BUT What I am NOT understanding Specifically is why 1346.8 = 6734 divided by 5 and why that is divided by 5 multiplied by 999
and can you tell me or elaborate on what technique or property is being used. Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
F = 1.3481481481481...
1000F = 1348.1481481...
- 1F = - 1.3481481...
999F = 1346.8
F = 1346.8/999
Multiply by something to get integers.
You can use 10
F = 13468/9990
Then reduce
F = 182/135