# Round number

A round number is mathematically defined as an integer which is the product of a considerable number of comparatively small factors as compared to its neighboring 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).

A round number is informally considered to be an integer that ends with one or more "0"s (zero-digit) in a given base. So, 590 is rounder than 592, but 590 is less round than 600. In both technical and informal language, a round number is often interpreted to stand for a value or values near to the nominal value expressed. For instance, a round number such as 600 might be used to refer to a value whose magnitude is actually 592, because the actual value is more cumbersome to express exactly. Likewise, a round number may refer to a range of values near the nominal value that expresses imprecision about a quantity. Thus, a value reported as 600 might actually represent any value near 600, possibly as low as 550 or as high as 650, all of which would round to 600.

In decimal notation, a number ending in the digit "5" is also considered more round than one ending in another non-zero digit (but less round than any which ends with "0"). For example, the number 25 tends to be seen as more round than 24. Thus someone might say, upon turning 45, that their age is more round than when they turn 44 or 46. These notions of roundness are also often applied to non-integer numbers; so, in any given base, 2.3 is rounder than 2.297, because 2.3 can be written as 2.300. Thus, a number with fewer digits which are not trailing "0"s is considered to be rounder than others of the same or greater precision.

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 (base 2: 10000000000), octal (base 8: 2000), and hexadecimal (base 16: 400). The previous discussion about the digit "5" generalizes to the digit representing b/2 for base-b notation, if b is even.

## Psychology and sociology

Psychologically round numbers form waypoints in pricing and negotiation. So, starting salaries are usually round numbers. Prices are often pitched just below round numbers in order to avoid breaking such a psychological barrier.

## Culture

Round-number anniversaries are often especially celebrated. For example, a fiftieth birthday, the centenary of an event, or the millionth visitor or customer to a location or business.

## Round number bias

Round number bias refers to the psychological tendency for a person to prefer rounded numbers over numbers that aren't rounded, which is passed onto a person through socialization. Rounded numbers are also easier for a person to remember, process, and perform mathematical operations on.

Round number bias has been observed in American and Chinese stock markets and stock prices in general, in retail and grocery, where prices are often just slightly less than a rounded number (ex. \$9.99 or \$9.95), in investments, including crowdfunding, in the real estate market through mortgages, and number milestones. Round number bias is also the reason for the existence of the common misconception that the 3rd millennium and 21st century started on January 1, 2000, when in actuality, both started a year later on January 1, 2001.