Table of Contents

## What are divisible numbers by 9?

List of Numbers Divisible by 9. There are 11 numbers less than 100 that are divisible by 9: 9, 18, 27, 36, 45, 63, 72, 81, 90 and 99.

## How do you show that something is divisible by 9?

Theorem

- A number expressed in decimal notation is divisible by 9 if and only if the sum of its digits is divisible by 9.
- A number expressed in decimal notation is divisible by 3 if and only if the sum of its digits is divisible by 3.
- Let N be divisible by 9.

**Why does divisibility rule for 9 work?**

Why Does the Divisibility by 9 Test Work? To test for divisibility by 9, all you have to do is add up the digits of the number and check if that sum is divisible by 9. If it is, then the entire number is divisible by 9 too. If not, then the original number is not divisible by 9.

### Why does the 9 divisibility rule work?

### How do you cast out 9s in addition?

To “cast out nines” from a single number, its decimal digits can be simply added together to obtain its so-called digit sum. The digit sum of 2946, for example is 2 + 9 + 4 + 6 = 21. Since 21 = 2946 − 325 × 9, the effect of taking the digit sum of 2946 is to “cast out” 325 lots of 9 from it.

**Which divisibility rule is this if the sum of its digit is divisible by 9?**

Answer: The divisibility rule of 9 says that a number is divisible by 9 if the sum of the digits of the number is divisible by 9. Ex – 72 is divisible by 9 because 7 + 2 = 9. 108 is also divisible by 9 because 1 + 0 + 8 = 9.

## Why are transposition errors divisible by 9?

A transposition error occurs when an amount is recorded incorrectly as the result of switching the positions of two (or more) digits. The switching of the positions causes a difference (between the recorded amount and the correct amount) that will be evenly divisible by 9.

## What is the pattern of 9?

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108. After listing the multiples of nine up to 108, we added the digits of each multiple and discovered that each answer was equal to 9 (with 99; 9 + 9 = 18; then 1 + 8 = 9).