Which Fractions 1/n have a
terminating decimal expansion?
When does 1/n terminate in other number systems?
Before we can tackle this question, we will first talk about our number system. Our number system is a decimal system; this can also be said as a base 10 number system. This means that we count by powers of ten. This seems like a logical base to use because humans have ten fingers. Thus, a decimal number system developed because humans have a habit of counting on their fingers. Before you move on to the next paragraph you should think of the results we acquired in our proof and the prime factors of 10.
Would we get the same result if we were using a different base?
No, we would not. If we were in a base 6 number system, 1/n would only terminate if and only if the prime factors of n are 2 and 3. Notice that 2 and 3 are the prime factors of 6.
cool trivia: the Babylonians had a base 60 number system.