Final answer:
The correct answer is option a. The digit that appears the smallest number of times when writing down all whole numbers from 1 to 1000 is 0 since it's less frequently used in number formation, particularly at the start of numbers.
Step-by-step explanation:
The question involves determining which digit appears the smallest number of times when all the whole numbers from 1 to 1000 inclusive are written down.
When we list out all the numbers in this range, every digit from 1 to 9 would appear with roughly the same frequency in each place value except for zero, which wouldn't appear in the thousands place at all and would be less common in the hundreds, tens, and ones places since numbers don't start with zero. However, since the question suggests single digits, and zero is not written in units place for numbers less than 10, it would occur less frequently in the context.
Therefore, the digit that would appear the smallest number of times is 0, because it is not used as frequently as other digits. The other digits from 1 to 9 appear in a more uniform distribution including the hundreds, tens, and units place. Thus, the correct option is a. 0.