What is the rule for a number to be divisible by 9?

The rule for a number to be divisible by 9 is that the sum of its digits must be divisible by 9. This means that if you take any number and add all of its individual digits together, the resulting sum must be a multiple of 9 for the original number to also be divisible by 9. For example, if you have the number 729, you would add 7 + 2 + 9, which equals 18. Since 18 is divisible by 9, the original number 729 is also divisible by 9.

This rule works because of the properties of the decimal system and how numbers are structured. When a number is expressed in a base (like base 10), the divisibility rules often relate to the sum of the digits due to the way that the digits represent multiples of powers of ten, which are congruent to 1 mod 9. Thus, checking the sum of the digits becomes a practical and quick way to determine divisibility by 9.

The other options, while they may refer to other divisibility rules or properties of numbers, do not accurately specify the condition for divisibility by 9.