How many 100 digit positive number are there ?

Options

A. `9xx10^(99)`
B. `9xx10^(100)`
C. `10100`
D. `11xx10^(98)`

Answer

To find out how many 100-digit positive numbers there are, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Understanding the Structure of a 100-Digit Number**:
A 100-digit positive number cannot start with the digit 0. Therefore, the first digit must be between 1 and 9.

2. **Choosing the First Digit**:
Since the first digit can be any digit from 1 to 9, there are 9 possible choices for the first digit.

3. **Choosing the Remaining Digits**:
The remaining 99 digits can be any digit from 0 to 9. This gives us 10 possible choices for each of the remaining digits.

4. **Calculating the Total Combinations**:
- For the first digit, there are 9 choices.
- For each of the remaining 99 digits, there are 10 choices.
- Therefore, the total number of 100-digit positive numbers can be calculated as:
\[ \text{Total Numbers} = (\text{Choices for First Digit}) \times (\text{Choices for Remaining Digits})^{\text{Number of Remaining Digits}} \]
\[ \text{Total Numbers} = 9 \times 10^{99} \]

5. **Final Answer**:
Thus, the total number of 100-digit positive numbers is \( 9 \times 10^{99} \).