Final answer:
To express the first 15 counting numbers in base nine, count from 1 to 8 using base nine digits, then continue with 10, 11, up to 16, which correspond to the base ten counting numbers 1 to 15.
Step-by-step explanation:
The question requires expressing the first 15 counting numbers in base nine. In base nine, the digits used are 0, 1, 2, 3, 4, 5, 6, 7, and 8. We start counting in base nine just as we do in base ten, but once we hit the digit '8', instead of moving to '9' we shift the leftmost digit by one and reset the rightmost digit back to '0', indicating that we've started counting in a new set.
- The first 15 counting numbers in base nine are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, and 16.
This corresponds to the base ten numbers 1 to 15 respectively. It is important to note that the numbers in base nine do not include a '9', because that is not a valid digit in this base; the equivalent to '9' in base ten is represented as '10' in base nine.