Each question has four options(A), (B), (C) and (D) for answers. Select the right answer and write in English letters in the box against each question in the enclosed answer sheet.
The sum of all the digits of the numbers from 1 to 100 is

Options

A. 5050
B. 903
C. 901
D. 900

Answer

To find the sum of all the digits of the numbers from 1 to 100, we can break it down into manageable steps.

### Step-by-Step Solution:

1. **Identify the Range**: We need to find the sum of the digits of all numbers from 1 to 100.

2. **Break Down the Numbers**: We can separate the numbers into two parts:
- Numbers from 1 to 9
- Numbers from 10 to 99
- The number 100

3. **Calculate the Sum of Digits from 1 to 9**:
- The digits are: 1, 2, 3, 4, 5, 6, 7, 8, 9.
- The sum is:
\[ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 \]

4. **Calculate the Sum of Digits from 10 to 99**:
- For each ten (10-19, 20-29, ..., 90-99), we can calculate the contribution of the tens and units separately.
- **Tens Contribution**:
- From 10 to 19: 1 contributes 10 times (1 for each number).
- From 20 to 29: 2 contributes 10 times.
- Continue this until 90 to 99 where 9 contributes 10 times.
- So, the tens contribution is:
\[ 10(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 10 \times 45 = 450 \]
- **Units Contribution**:
- Each digit from 0 to 9 appears 9 times (once for each ten).
- So, the units contribution is:
\[ 9(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 9 \times 45 = 405 \]

5. **Combine the Contributions**:
- Total from 10 to 99:
\[ 450 + 405 = 855 \]

6. **Add the Contribution from 100**:
- The digits of 100 are 1, 0, and 0, which sum up to:
\[ 1 + 0 + 0 = 1 \]

7. **Final Sum**:
- Combine all the sums:
\[ 45 + 855 + 1 = 901 \]

### Final Answer:
The sum of all the digits of the numbers from 1 to 100 is **901**.