A round number is mathematically defined as the product of a considerable number of comparatively small factors[1] as compared to its neighbouring numbers, such as 24 = 2*2*2*3 (4 factors, as opposed to 3 factors for 27; 2 factors for 21, 22, 25, and 26; and 1 factor for 23).
However, a round number is informally considered to be an integer that ends with one or more zeroes (0), such as 1,000, 1,500,000, etc., and a number ending in 5 might be considered in a way more "round" than one ending in neither 0 nor 5. Even a non-integer such as 2.5 might be seen as more round than, say, 2.497 (especially if written as 2.500).
When a quantity is known only to a low precision, a calculation that gives a non-round number is oftentimes rounded in order to avoid giving a false impression of accuracy.
When counting or measuring, people usually view a roll-over to a round number as a milestone. This fascination led people to celebrate a new millennium at the beginning of the year 2000, even though the official millennium change didn't occur until 2001. A roll-over that adds another digit is often seen as particularly exciting.
Numbers can also be considered "round" in numbering systems other than decimal (base 10). For example, the number 1024 would not be considered "round" in decimal, but the same number ends with a zero in several other numbering systems including binary, octal, and hexadecimal.