The Digit Sum
The word digit means a single figure number: the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0.
Sum means add.
The digit sum of a number is found by adding the digits in the number.
To find the digit sum of 17, for example, you just add the 1 and 7.
1 + 7 = 8, so the digit sum of 17 is 8.
And the digit sum of 123 is 6 because 1+2+3=6.
The digit sum is found by adding the digits in a number,
and adding again if necessary
So for the digit sum of 19 you add 1 + 9 = 10.
But since 10 is a 2-digit number you add again: 1+0 = 1.
So for the digit sum of 19 you can write:
19 - 10 - 1
Similarly for 39 you get 39 - 12 - 3.
So the digit sum of 39 is 3.
Find the digit sum of the following numbers:
83 614 345 5555 78 2379 521832 999
Casting out nine
Adding 9 to a number does not affect its digit sum:
so 4, 40, 49, 94, 949 all have a digit sum of 4 for example.
Any group of figures in a number that add up to 9 can be "cast out".
To find the digit sum of 24701 you see that you have 2 and 7 which add up to 9 and can therefore be cast out. This leaves only 4 and 1 which add up to 5. So the digit sum of 24701 is 5.
Find the digit sum of the following numbers:
2346 16271 9653 36247 215841 7152 9821736
Digit sums can be very useful: for checking calculations , in divisibility testing, in finding square roots; and there is an algebraic form too
पोस्ट्स
कोणत्याही टिप्पण्या नाहीत:
टिप्पणी पोस्ट करा
comment