Generally speaking, a round number is a number that ends with one or more zeroes (0), meaning that they are multiples of 10, 100, 1000, and so on. There are variations on this theme, where multiples of 5 or 25 might also be considered "round." When counting and measuring, people often view the rollover to a round number as something of great importance. For example, a family might gather in their automobile to view the moment the vehicle's odometer goes from 49,999 to 50,000 or 99,999 to 100,000. A rollover that adds another digit is often seen as particularly exciting. A similar fascination led people around the world to celebrate a new millennium at the beginning of the year 2000, even though the event wouldn't really occur until the end of that year and the beginning of 2001.
Numbers can also be considered as "round" in numbering systems other than decimal (base 10). For example the number 32 is not round in decimal, but ends with zero in several bases including binary and hexadecimal.
See also