The number of times the digit 0 is used in writing the numbers from 1 to 1000 is equal to

Options

A. 189
B. 300
C. 192
D. 270

Answer

To find the total number of times the digit '0' is used when writing the numbers from 1 to 1000, we can break down the problem into manageable parts.

### Step 1: Count the occurrences of '0' in different ranges of numbers.

1. **Single-digit numbers (1 to 9)**:
- There are no occurrences of '0' in this range.
- **Count = 0**

2. **Two-digit numbers (10 to 99)**:
- The digit '0' can only appear in the units place (e.g., 10, 20, 30, ..., 90).
- The numbers are: 10, 20, 30, 40, 50, 60, 70, 80, 90.
- There are 9 occurrences of '0'.
- **Count = 9**

3. **Three-digit numbers (100 to 999)**:
- The digit '0' can appear in the tens and units places.
- **Case 1: '0' in the tens place**:
- The numbers are: 100, 101, 102, ..., 109; 200, 201, ..., 209; ..., 900, 901, ..., 909.
- For each hundred (100-199, 200-299, ..., 900-999), there are 10 occurrences of '0' (100-109, 200-209, ..., 900-909).
- There are 9 hundreds, so total occurrences = 9 * 10 = 90.
- **Case 2: '0' in the units place**:
- The numbers are: 100, 110, 120, ..., 190; 200, 210, ..., 290; ..., 900, 910, ..., 990.
- For each hundred, there are 10 occurrences of '0' (100, 110, 120, ..., 190).
- Again, there are 9 hundreds, so total occurrences = 9 * 10 = 90.
- **Total for three-digit numbers = 90 (tens) + 90 (units) = 180**

4. **The number 1000**:
- The number 1000 contains three '0's.
- **Count = 3**

### Step 2: Sum all the counts from each range.

- Total occurrences of '0' = Count from single-digit numbers + Count from two-digit numbers + Count from three-digit numbers + Count from 1000
- Total occurrences of '0' = 0 + 9 + 180 + 3 = 192

### Final Answer:
The total number of times the digit '0' is used in writing the numbers from 1 to 1000 is **192**.

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