SOLUTION: For how many values of n where n≤100 is 1/n represented by a terminating decimal?

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Question 326015: For how many values of n where n≤100 is 1/n represented by a terminating decimal?
Found 2 solutions by Edwin McCravy, Fombitz:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
For how many values of n where n≤100 is 1/n represented by a terminating decimal?

 will be a terminating decimal if and only if 
its only prime factors are 2 and 5 (the prime factors of 10)

all the powers of 2 under 100 are

2, 4, 8, 16, 32, 64

That's the first set of numbers

all the powers of 5 under 100 are

5, 25

1 over any of those will be a terminating decimal.

But that's not all,

1 over any product of those will also be a terminating decimal.

Now we get all the products of one of the first set
times one of the numbers in the second set.

the only products of those are

2*5=10, 4*5=20, 8*5=40, 16*5=80, (32x5 is over 100 so we stop)

2*25=50, 4*25=100, (8*25 is over 100 so we stop)

So the only cases are

 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8.  
 9. 
10. 
11. 
12. 
13. 
14. 

So there are 14.

Edwin
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Fifteen times (1,2,4,5,8,10,16,20,25,32,40,50,64,80,100)
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