How many times does the digit 9 occur between 1 and 100 ?

Options

A. 11
B. 15
C. 18
D. 20

Answer

To find out how many times the digit 9 occurs between 1 and 100, we can break it down step by step.

### Step-by-Step Solution:

1. **Count occurrences of 9 in each decade:**
- **From 1 to 10:** The digit 9 appears **1 time** (in the number 9).
- **From 11 to 20:** The digit 9 appears **1 time** (in the number 19).
- **From 21 to 30:** The digit 9 appears **1 time** (in the number 29).
- **From 31 to 40:** The digit 9 appears **1 time** (in the number 39).
- **From 41 to 50:** The digit 9 appears **1 time** (in the number 49).
- **From 51 to 60:** The digit 9 appears **1 time** (in the number 59).
- **From 61 to 70:** The digit 9 appears **1 time** (in the number 69).
- **From 71 to 80:** The digit 9 appears **1 time** (in the number 79).
- **From 81 to 90:** The digit 9 appears **2 times** (in the numbers 89 and 90).
- **From 91 to 100:** The digit 9 appears **10 times** (in the numbers 91, 92, 93, 94, 95, 96, 97, 98, 99, and 100).

2. **Add up all the occurrences:**
- From 1 to 10: 1
- From 11 to 20: 1
- From 21 to 30: 1
- From 31 to 40: 1
- From 41 to 50: 1
- From 51 to 60: 1
- From 61 to 70: 1
- From 71 to 80: 1
- From 81 to 90: 2
- From 91 to 100: 10

Now, let's total these occurrences:
\[ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 10 = 20 \]

3. **Conclusion:**
- The digit 9 occurs **20 times** between 1 and 100.