Find the number of odd positive three digit integers.

Explanation

To find the number of odd positive three-digit integers, we can break down the problem step by step.

### Step 1: Identify the Structure of a Three-Digit Integer
A three-digit integer can be represented as \(abc\), where:
- \(a\) is the hundreds place,
- \(b\) is the tens place,
- \(c\) is the units place.

### Step 2: Determine the Units Place
Since we are looking for odd integers, the units place \(c\) must be filled with an odd digit. The possible odd digits are:
- 1
- 3
- 5
- 7
- 9

Thus, there are **5 choices** for the units place \(c\).

### Step 3: Determine the Hundreds Place
The hundreds place \(a\) cannot be 0 (as it is a three-digit number). Therefore, the possible digits for \(a\) are:
- 1, 2, 3, 4, 5, 6, 7, 8, 9

This gives us **9 choices** for the hundreds place \(a\).

### Step 4: Determine the Tens Place
The tens place \(b\) can be any digit from 0 to 9. Therefore, there are **10 choices** for the tens place \(b\).

### Step 5: Calculate the Total Number of Odd Positive Three-Digit Integers
Now, we can calculate the total number of odd positive three-digit integers by multiplying the number of choices for each digit:
\[ \text{Total} = (\text{Choices for } a) \times (\text{Choices for } b) \times (\text{Choices for } c) \]
\[ \text{Total} = 9 \times 10 \times 5 \]
\[ \text{Total} = 450 \]

Thus, the total number of odd positive three-digit integers is **450**.