document.write( "Question 326015: For how many values of n where n≤100 is 1/n represented by a terminating decimal? \n" ); document.write( "
Algebra.Com's Answer #233379 by Edwin McCravy(20056)\"\" \"About 
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For how many values of n where n≤100 is 1/n represented by a terminating decimal?
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document.write( "\"1%2Fn\" will be a terminating decimal if and only if \r\n" );
document.write( "its only prime factors are 2 and 5 (the prime factors of 10)\r\n" );
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document.write( "all the powers of 2 under 100 are\r\n" );
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document.write( "2, 4, 8, 16, 32, 64\r\n" );
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document.write( "That's the first set of numbers\r\n" );
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document.write( "all the powers of 5 under 100 are\r\n" );
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document.write( "5, 25\r\n" );
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document.write( "1 over any of those will be a terminating decimal.\r\n" );
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document.write( "But that's not all,\r\n" );
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document.write( "1 over any product of those will also be a terminating decimal.\r\n" );
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document.write( "Now we get all the products of one of the first set\r\n" );
document.write( "times one of the numbers in the second set.\r\n" );
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document.write( "the only products of those are\r\n" );
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document.write( "2*5=10, 4*5=20, 8*5=40, 16*5=80, (32x5 is over 100 so we stop)\r\n" );
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document.write( "2*25=50, 4*25=100, (8*25 is over 100 so we stop)\r\n" );
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document.write( "So the only cases are\r\n" );
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document.write( " 1. \"1%2F2=.5\"\r\n" );
document.write( " 2. \"1%2F4=.25\"\r\n" );
document.write( " 3. \"1%2F8=.125\"\r\n" );
document.write( " 4. \"1%2F16=.0625\"\r\n" );
document.write( " 5. \"1%2F32=.03125\"\r\n" );
document.write( " 6. \"1%2F64=.015625\"\r\n" );
document.write( " 7. \"1%2F5=.2\"\r\n" );
document.write( " 8. \"1%2F25=.04\" \r\n" );
document.write( " 9. \"1%2F10=.1\"\r\n" );
document.write( "10. \"1%2F20=.05\"\r\n" );
document.write( "11. \"1%2F40=.025\"\r\n" );
document.write( "12. \"1%2F80=.0125\"\r\n" );
document.write( "13. \"1%2F50=.02\"\r\n" );
document.write( "14. \"1%2F100=.01\"\r\n" );
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document.write( "So there are 14.\r\n" );
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document.write( "Edwin

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