There are exactly 5,000 odd numbers between 1 and 10,000.
Understanding Odd Numbers
An odd number is any integer that is not divisible by 2. When an odd number is divided by 2, it leaves a remainder of 1. Odd numbers always end with one of the following digits: 1, 3, 5, 7, or 9.
For example:
- 1, 3, 5, 7, 9 are the first five odd numbers.
- 101, 247, 9999 are also odd numbers.
Determining the Count of Odd Numbers in a Range
When counting numbers in a consecutive range starting from 1, odd and even numbers typically alternate. This means that, for a given range from 1 to a number 'N', approximately half of the numbers will be odd and half will be even.
Specifically:
- If 'N' is an even number, the count of odd numbers from 1 to N is exactly N/2.
- If 'N' is an odd number, the count of odd numbers from 1 to N is (N+1)/2.
In the case of the range from 1 to 10,000, since 10,000 is an even number, the count of odd numbers is 10,000 / 2 = 5,000.
Reference Data from Byju's
The information provided by Byju's directly supports this calculation, illustrating the pattern for various number ranges:
Number Range | No. of Odd Numbers |
---|---|
1 to 300 | 150 |
1 to 500 | 250 |
1 to 1000 | 500 |
1 to 10000 | 5000 |
Source: Odd Numbers (Definition, Chart, Properties & Solved Examples) byjus.com
As the table clearly indicates, for the range from 1 to 10,000, there are 5,000 odd numbers.
Exact Answer
Based on the properties of odd numbers and confirmed by the provided reference, the exact number of odd integers between 1 and 10,000 (inclusive of 1, as it is an odd number, and considering the full range up to 10,000) is 5,000.