For how many integer values of $n$ between 1 and 1000 inclusive does the decimal representation of $/frac{n}{1400}$ terminate?

Question

Luke Schaefer

Computers & Technology

18 March, 16:09

For how many integer values of $n$ between 1 and 1000 inclusive does the decimal representation of $/frac{n}{1400}$ terminate?

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Answers (1)

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Ava Arias · Answer 1

142 integers

Explanation:

For the given expression "n/1400", there exists a terminating expansion if and on if 2 and 5 are in the denominator. Therefore:

The denominator "1400" can be broken down into (2^3) * (5^2) * 7. Then we need a number that can be divided by 7 and is between 1 and 1000. The number is 994 and the number of possible integer values = 994/7 = 142.