Final answer:
To determine if a natural number with up to 9 digits is divisible by 3, sum its digits and check if the sum is divisible by 3. A 9-digit number like 123,456,789 is divisible by 3 because its digits sum to 45, which is divisible by 3.
Step-by-step explanation:
To determine if a number is divisible by 3, you sum up all its digits and check whether this sum is divisible by 3. For any natural number with up to 9 digits, there is a possibility that it contains numbers divisible by 3. If the sum of these digits is divisible by 3, then the number itself is divisible by 3.
As an example, consider the 9-digit number 123,456,789. The sum of its digits is 1+2+3+4+5+6+7+8+9=45, which is divisible by 3. Therefore, the number 123,456,789 is divisible by 3. This method can be applied to any natural number regardless of its length, as long as we know its digits.
Another key concept related to divisibility is cubing of exponentials. When cubing an exponential term, you cube the base and multiply the exponent by 3. However, this process does not help determine divisibility by 3 for the nine-digit number in question.