document.write( "Question 911664: All the odd numbers from 51 to 5001 are written. What is the total numbers of digit used? \n" ); document.write( "
Algebra.Com's Answer #553354 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "I redid this problem. For some strange reason I didn't notice that it said \"odd \r\n" );
document.write( "numbers\" and I did it for all the numbers.  I don't know why I didn't see it,\r\n" );
document.write( "It says \"odd\" plain as day!  Anyway, my bad.  It's the same principle, only a\r\n" );
document.write( "little harder.  Here's my approach:\r\n" );
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document.write( "2-digit numbers:\r\n" );
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document.write( "The sequence of odd numbers:\r\n" );
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document.write( "51, 53, 55, ..., 97, 99\r\n" );
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document.write( "have 2 digits each.  There are the same number of those as there are\r\n" );
document.write( "numbers which are 1 less than them, which are these:\r\n" );
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document.write( "50, 52, 54, ..., 96, 98, \r\n" );
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document.write( "There are the same number of those as there are\r\n" );
document.write( "numbers which are half of them, which are these:\r\n" );
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document.write( "25, 26, 27, ..., 48, 49  \r\n" );
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document.write( "These are the 49 numbers 1 through 49, minus the 24 numbers 1 through 24\r\n" );
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document.write( "and 49-24 = 25\r\n" );
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document.write( "So there are 25 numbers with 2 digits each, so the number of digits in\r\n" );
document.write( "the 2-digit numbers in the original sequence is 2x25 or 50.\r\n" );
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document.write( "3-digit numbers:\r\n" );
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document.write( "The sequence of odd numbers:\r\n" );
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document.write( "101, 103, 105, ..., 997, 999\r\n" );
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document.write( "have 3 digits each.  There are the same number of those as there are\r\n" );
document.write( "numbers which are 1 less than them, which are these:\r\n" );
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document.write( "100, 102, 104, ..., 996, 998, \r\n" );
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document.write( "There are the same number of those as there are\r\n" );
document.write( "numbers which are half of them, which are these:\r\n" );
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document.write( "50, 51, 52, ..., 498, 499  \r\n" );
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document.write( "These are the 499 numbers 1 through 499, minus the 49 numbers 1 through 49\r\n" );
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document.write( "and 499-49 = 450\r\n" );
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document.write( "So there are 450 numbers with 3 digits each, so the number of digits in\r\n" );
document.write( "the 3-digit numbers in the original sequence is 3x450 or 1350.\r\n" );
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document.write( "4-digit numbers:\r\n" );
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document.write( "The sequence of odd numbers:\r\n" );
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document.write( "1001, 1003, 1005, ..., 4999, 5001\r\n" );
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document.write( "have 4 digits each.  There are the same number of those as there are\r\n" );
document.write( "numbers which are 1 less than them, which are these:\r\n" );
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document.write( "1000, 1002, 1004, ..., 4998, 5000, \r\n" );
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document.write( "There are the same number of those as there are\r\n" );
document.write( "numbers which are half of them, which are these:\r\n" );
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document.write( "500, 501, 502, ..., 2499, 2500  \r\n" );
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document.write( "These are the 2500 numbers 1 through 2500, minus the 499 numbers 1 through\r\n" );
document.write( "499\r\n" );
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document.write( "and 2500-499 = 2001\r\n" );
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document.write( "So there are 2001 numbers with 4 digits each, so the number of digits in\r\n" );
document.write( "the 4-digit numbers in the original sequence is 4x2001 or 8004.\r\n" );
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document.write( "Grand total: 50 + 1350 + 8004 = 9404 digits.\r\n" );
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document.write( "Edwin
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