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#1 2008-03-09 02:47:47
- chetah
- Member
- Registered: 2008-02-15
- Posts: 32
Discrete Mathematics
Write 0.09 (the 9 is recurring) as a fraction. My answer is 81/900. My text answer is 1/10. Where did I go wrong?
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#2 2008-03-09 03:03:46
- Daniel123
- Member
- Registered: 2007-05-23
- Posts: 663
Re: Discrete Mathematics
Let r = 0.0999999...
100r = 9.9999999...
99r = 100r - r
= 9.99999... - 0.0999...
= 9.9
If 99r = 9.9
990r = 99
r = 99/990
= 1/10
EDIT: 81/900 is not a recurring fraction. 81/900 = 9/100 = 0.09
Last edited by Daniel123 (2008-03-09 03:08:46)
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#3 2008-03-09 04:47:29
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Discrete Mathematics
1/30 = 0.0333333....
1/30 * 3 = 0.0999999.....
But 1/30*3 = 1/10
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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