Prime Factors in Unit Fractions
Date: 2/29/96 at 2:31:48 From: gary roberts Subject: terminating decimals Why does the denominator of a unit fraction have to have prime factors of 2 and/or 5 in order to terminate? :-)
Date: 3/1/96 at 13:3:42 From: Doctor Ethan Subject: Re: terminating decimals Well, the easy answer is that those are the prime factors of ten, but let's see why that makes sense. When you write numbers out as decimals you are essentially looking at them as a series of fractions. For instance: .13278 is 1/10 + 3/100 + 2/1000 + 7/10000 + 8/100000 Or 13278 ------ 100000 Does that makes sense? So when you have a fraction, it can be written as a finite decimal if and only if it can be written as a fraction in the form of n/ 10^k that is some integer n divided by 10 to some power. So for instance 3/25 = 12/100 = .12 or 7/16 = 35/80 = 175/400 = 875/2000 = 4375/10000 = .4375 However, if we had 3/7 then no multiplying by stuff on the top and bottom will ever make the bottom equal to a power of ten. Does this make any sense? If you want more help then write back to us. -Doctor Ethan, The Math Forum
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