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For how many integer values between 1 and 1,000 does the decimal representation of their reciprocals terminate?
Examples: 1/2 =0.5, 1/25 =0.04, 1/256 =0.00390625........etc.
Thanks for help.

 Oct 6, 2018
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All powers of 2 up to 1,000(1,2,3,4,5,6,7,8,9)
All powers of 5 up to 1,000(1,2,3,4)
All powers of 2 x 5 up to 1,000
2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^8, 2^9
5^1, 5^2, 5^3, 5^4
2^1*5, 2^2*5, 2^3*5, 2^4*5, 2^5*5, 2^6*5, 2^7*5
2^1*5^2, 2^1*5^3
2^2*5^2, 2^2*5^3
2^3*5^2, 2^3*5^3
2^4*5^2
2^5*5^2
(2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1 000)=28 Numbers between 1 and 1000 whose reciprocals have a terminating decimal.

 Oct 7, 2018

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