A round number is mathematically defined as the product of a considerable number of comparatively small factors 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

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

 that ends with one or more zero

0 (number)

0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...

es (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

Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.Rounding is often done on purpose to...

 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

Millennium

A millennium is a period of time equal to one thousand years —from the Latin phrase , thousand, and , year—often but not necessarily related numerically to a particular dating system....

 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

Numerical digit

A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

 is often seen as particularly exciting.

Numbers can also be considered "round" in numbering systems

Numeral system

A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....

 other than decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 (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

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

, octal

Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

, and hexadecimal

Hexadecimal

In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...

.