To find out how many times the digit '2' appears in the first 100 natural numbers, we can break down the counting process step by step.
### Step-by-Step Solution:
1. **Count from 1 to 9**:
- The numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9.
- The digit '2' appears **1 time** (in the number 2).
2. **Count from 10 to 19**:
- The numbers are: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
- The digit '2' appears **1 time** (in the number 12).
3. **Count from 20 to 29**:
- The numbers are: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
- The digit '2' appears **11 times** (1 time in 20, 1 time in 21, 2 times in 22, and 1 time each in 23, 24, 25, 26, 27, 28, 29).
4. **Count from 30 to 39**:
- The numbers are: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
- The digit '2' appears **1 time** (in the number 32).
5. **Count from 40 to 49**:
- The numbers are: 40, 41, 42, 43, 44, 45, 46, 47, 48, 49.
- The digit '2' appears **1 time** (in the number 42).
6. **Count from 50 to 59**:
- The numbers are: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59.
- The digit '2' appears **1 time** (in the number 52).
7. **Count from 60 to 69**:
- The numbers are: 60, 61, 62, 63, 64, 65, 66, 67, 68, 69.
- The digit '2' appears **1 time** (in the number 62).
8. **Count from 70 to 79**:
- The numbers are: 70, 71, 72, 73, 74, 75, 76, 77, 78, 79.
- The digit '2' appears **1 time** (in the number 72).
9. **Count from 80 to 89**:
- The numbers are: 80, 81, 82, 83, 84, 85, 86, 87, 88, 89.
- The digit '2' appears **1 time** (in the number 82).
10. **Count from 90 to 99**:
- The numbers are: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
- The digit '2' appears **1 time** (in the number 92).
11. **Count the number 100**:
- The number is 100.
- The digit '2' appears **0 times**.
### Total Count:
Now we can sum up all the occurrences:
- From 1 to 9: 1
- From 10 to 19: 1
- From 20 to 29: 11
- From 30 to 39: 1
- From 40 to 49: 1
- From 50 to 59: 1
- From 60 to 69: 1
- From 70 to 79: 1
- From 80 to 89: 1
- From 90 to 99: 1
- From 100: 0
Adding these together:
1 + 1 + 11 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 0 = **20 times**.
### Final Answer:
The digit '2' appears **20 times** in the first 100 natural numbers.
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