There are 5,000 odd numbers between 1 and 10,000.
Understanding Odd Numbers
Odd numbers are integers that are not divisible by 2. They leave a remainder of 1 when divided by 2. The sequence of odd numbers starts with 1, 3, 5, 7, and so on.
Calculating the Number of Odd Numbers
To determine the number of odd numbers between 1 and 10,000, we can observe a pattern:
- Between 1 and 10, there are 5 odd numbers (1, 3, 5, 7, 9).
- Between 1 and 100, there are 50 odd numbers.
- Between 1 and 1,000, there are 500 odd numbers.
Following this pattern, between 1 and 10,000, half of the numbers will be odd and half will be even.
Therefore, the number of odd numbers is 10,000 / 2 = 5,000.
| Number Range | Number of Odd Numbers |
|---|---|
| 1 to 10 | 5 |
| 1 to 100 | 50 |
| 1 to 1,000 | 500 |
| 1 to 10,000 | 5,000 |
Therefore, there are exactly 5,000 odd numbers between 1 and 10,000.
