# Topic 6: Digit Sums

What is a digit?

“Digit” is derived from Latin word digitus meaning ‘finger, toe’. Digit means any numeral below 10, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

A “Digit Sum” is the sum of all of the digits of a number, and is found by adding all of the digits of a number.

For example:

1. The Digit Sum of 32 is 3+2 = 5
2. The Digit Sum of 152 is 1+5+2 = 8

If the sum of the digits is greater than 9, then sum the digits of the result again until the result is less than 10.

For example:

1. The Digit Sum of 57 is 5+7 = 12 → 1+2 = 3 ….. Here 12 >9, so sum the digits again.
So the Digit Sum of 57 is 3.
2. The Digit Sum of 687 is 6+8+7 = 21 → 2+1 = 3…. Here 21 >9, so sum the digits again.
So the Digit Sum of 687 is 3.

Keep finding the Digit Sum of the result until it’s less than 10. Also, in case of digit sum, 0 and 9 are equivalent!

Why is digit sum important?

Digit sum is used for checking calculations, and this becomes highly useful where large numbers are involved. I will explain this part in subsequent sections.

In this course, we are going to study about below topics:

• Nine Point Circle
• Casting Out nines (9s)
• Checking with Digit Sums
• A magic number