To determine which digit is written the least number of times when writing all numbers from 1 to 100 (both included), follow the steps below:
1. Identify the Range and Numbers:
- Consider the range from 1 to 100.
2. List Digits from 0 to 9:
- The digits of interest are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
3. Count Each Digit:
- We need to count how many times each digit appears in the sequence of numbers from 1 to 100.
4. Break Down the Numbers:
- Analyze occurrences for each digit:
- 0: Appears in numbers like 10, 20, ..., 90, and 100.
- 1: Appears in 1, 10, 11, 12, 13, ..., 19, 21, 22, ..., 91, 100.
- 2: Appears in 2, 12, 20, 21, 22, 23, ..., 29, 32, ..., 92.
- Continue counting similarly for digits 3 through 9.
5. Tabulate Counts:
- Summarize the frequencies:
- 0: 11 times
- 1: 21 times
- 2: 20 times
- 3: 20 times
- 4: 20 times
- 5: 20 times
- 6: 20 times
- 7: 20 times
- 8: 20 times
- 9: 20 times
6. Determine the Least Frequent Digit:
- Inspect the counts: `0` appears 11 times, which is the least when compared to other digits.
Therefore, when writing all numbers from 1 to 100, the digit that would be written the least number of times is `0`.
