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Question 257912: What is the sum of all the digits of all the positive integers that are less than 100?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the positive digits are 1 through 9.
0 is a non-negative digits.
0 is not a positive digit.
when we sum up the digits it won't matter if we include 0 or not because the sum of all 0's is still 0.
when you count to 100, you have 1 set of tens digits and 1 set of units digits.
the total set of digits is shown in the following table:
00 10 20 30 40 50 60 70 80 90
01 11 21 31 41 51 61 71 81 91
02 12 22 32 42 52 62 72 82 92
03 13 23 33 43 53 63 73 83 93
04 14 24 34 44 54 64 74 84 94
05 15 25 35 45 55 65 75 85 95
06 16 26 36 46 56 66 76 86 96
07 17 27 37 47 57 67 77 87 97
08 18 28 38 48 58 68 78 88 98
09 19 29 39 49 59 69 79 89 99
the ones digits are on the right of each number.
the tens digits are on the left of each number.
example:
number 49:
9 is the ones digit
4 is the tens digit
to sum up all the digits, we sum up all the ones digits and all the tens digits separately and then add them together.
within each column, the ones digits add up to 45. that would be the sum of 1 through 9.
within each column, the tens digits add up to 10 * the digit shown. that would be 10 * 1, 10 * 2, etc.
you get the following number:
sum of tens digit sum of units digit total
from 0 to 9 0 45 45
from 10 to 19 10 45 55
from 20 to 29 20 45 65
from 30 to 39 30 45 75
from 40 to 49 40 45 85
from 50 to 59 50 45 95
from 60 to 69 60 45 105
from 70 to 79 70 45 115
from 80 to 89 80 45 125
from 90 to 99 90 45 135
total 450 450 900
sume of all the positive digits less than 100 is equal to 900.
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