Short Answer 
The number one appears once as a single-digit number (1) and 10 times in the two-digit range (10-19), totaling 11 occurrences from 1 to 30.
Step 1: Identify Single-Digit Occurrence
The first step is to recognize that the number one appears as a single-digit number. In the range of numbers from 1 to 30, the number one appears once, which is at the number 1 itself. This sets the foundation for counting its occurrences.
Step 2: Count the Occurrences in Two-Digit Numbers
Next, we need to account for the appearances of the number one in two-digit numbers. The relevant range is from 10 to 19. The number one occurs in these specific numbers:
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
In total, the number one appears 10 times in this segment of two-digit numbers.
Step 3: Add the Occurrences Together
Finally, to determine the total occurrences of the number one in the list of numbers from 1 to 30, we add the occurrences from both steps. We have:
- 1 occurrence from the single-digit number
- 10 occurrences from the two-digit numbers
When we add them together (1 + 10), we find that the number one appears a total of 11 times in the list.