Editing Round number

{{Short description|Integer ending in zeroes}}
{{Use dmy dates|date=August 2021}}
{{more citations needed|date=May 2012}}

A '''round number''' is an [[integer]] that ends with one or more "[[0 (number)|0]]"s (zero-digit) in a given [[Radix|base]].<ref>Sadock, J. M. (1977). Truth and approximation. ''Berkeley Linguistics Society Papers'' 3: 430–439.</ref> 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 [[Interval (mathematics)|range]] of values near the nominal value that expresses imprecision about a quantity.<ref name=Ferson-etal-2015>Ferson, S., J. O'Rawe, A. Antonenko, J. Siegrist, J. Mickley, C. Luhmann, K. Sentz, A. Finkel (2015). Natural language of uncertainty: numeric hedge words. ''International Journal of Approximate Reasoning'' 57: 19–39.</ref> Thus, a value reported as 600 might actually represent any value near 600, possibly as low as 550 or as high as 649, all of which would ''[[rounding|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").<ref name=Ferson-etal-2015 /><ref>de Lusignan, S., J. Belsey, N. Hague and B. Dzregah (2004). End-digit preference in blood pressure recordings of patients with ischaemic heart disease in primary care. ''Journal of Human Hypertension'' 18: 261–265.</ref> 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 [[Decimal#Decimal fractions|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 [[numeral system|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 numeral system|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 [[parity (mathematics)|even]].

==Psychology and sociology==
Psychologically, round numbers form [[Schelling point|waypoints]] in pricing and negotiation.  So, starting salaries are usually round numbers. Prices are often pitched [[Psychological pricing|just below round numbers]] to avoid breaking the psychological barrier of paying the price of the round number.

==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.

On January 1, 2000, the round-number year [[2000]] was [[Millennium celebrations|widely celebrated]]. Technically, the [[3rd millennium]] did not begin until January 1, 2001, a year later, as there is no [[year zero]] in the [[Gregorian calendar]].

== Round number bias ==
Round number bias is the [[psychological]] tendency to prefer round numbers over others,<ref name=":0">{{Cite web|last=Bikos|first=Konstantin|date=|title=When Did the 21st Century Start?|url=https://www.timeanddate.com/counters/mil2000.html|url-status=live|archive-url=https://web.archive.org/web/20201218094222/https://www.timeanddate.com/counters/mil2000.html|archive-date=18 December 2020|access-date=29 December 2020|website=timeanddate.com}}</ref><ref name=":1">{{Cite web|last=Vižintin|first=Žiga|date=6 February 2018|title=Why Five and Not Eight? How Round Number Bias Can Reduce Your Nest Egg|url=https://behavioralscientist.org/five-not-eight-round-number-bias-can-reduce-nest-egg/|url-status=live|archive-url=https://web.archive.org/web/20200804133150/https://behavioralscientist.org/five-not-eight-round-number-bias-can-reduce-nest-egg/|archive-date=4 August 2020|access-date=29 December 2020|website=Behavioral Scientist}}</ref> which is passed onto a person through socialization.<ref>{{Cite web|last=|first=|date=19 June 2017|title=How Round Number Bias and Psychological Pricing Affect Your Gains and Spending|url=https://dqydj.com/round-number-bias-psychological-pricing/|url-status=live|archive-url=https://archive.today/20201229212147/https://dqydj.com/round-number-bias-psychological-pricing/|archive-date=29 December 2020|access-date=29 December 2020|website=Don't Quit Your Day Job}}</ref> Round numbers are also easier for a person to remember, process, and perform [[mathematical operations]] on.<ref name=":1" />

Round number bias has been observed mainly in retail and [[Grocery store|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 [[milestone]]s.<ref name=":12">{{Cite web|last=Vižintin|first=Žiga|date=6 February 2018|title=Why Five and Not Eight? How Round Number Bias Can Reduce Your Nest Egg|url=https://behavioralscientist.org/five-not-eight-round-number-bias-can-reduce-nest-egg/|url-status=live|archive-url=https://web.archive.org/web/20200804133150/https://behavioralscientist.org/five-not-eight-round-number-bias-can-reduce-nest-egg/|archive-date=4 August 2020|access-date=29 December 2020|website=Behavioral Scientist}}</ref><ref>{{Cite journal|last1=Hervé|first1=Fabrice|last2=Schwienbacher|first2=Armin|date=January 2018|title=Round-Number Bias in Investment: Evidence from Equity Crowdfunding|url=https://www.cairn.info/revue-finance-2018-1-page-71.htm?ref=doi|journal=[[Finance (journal)|Finance]]|volume=39|page=71|doi=10.3917/fina.391.0071|archive-url=https://archive.today/20201229212548/https://www.cairn.info/revue-finance-2018-1-page-71.htm?ref=doi|archive-date=29 December 2020|via=cairn.info|access-date=21 January 2021|url-status=live|doi-access=free}}</ref><ref>{{Cite journal|last=Guo|first=Tiansheng|title=The Effect of Round Number Bias inU.S. and Chinese Stock Markets|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.670.6061&rep=rep1&type=pdf|journal=[[Michigan Journal of Business]]|pages=41–42|citeseerx=10.1.1.670.6061|archive-url=https://archive.today/20201229212735/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.670.6061&rep=rep1&type=pdf|archive-date=29 December 2020|via=[[CiteSeerX]]|access-date=21 January 2021|url-status=live}}</ref><ref>{{Cite journal|last1=L. Ross|first1=Stephen|last2=Zhou|first2=Tingyu|date=3 November 2020|title=Documenting Loss Aversion using Evidence of Round Number Bias|url=https://media.economics.uconn.edu/working/2020-17.pdf|journal=[[University of Connecticut]]|page=2|archive-url=https://web.archive.org/web/20201229213136/https://media.economics.uconn.edu/working/2020-17.pdf|archive-date=29 December 2020|via=uconn.edu}}</ref>

Round numbers are often used when estimating the time taken to complete a task.<ref>{{cite web|url=https://shape-of-code.coding-guidelines.com/2020/05/31/estimating-in-round-numbers/|title=Estimating in round numbers|accessdate=9 August 2021}}</ref>

==Mathematics==

A round number is mathematically defined as an [[integer]] which is the product of a considerable number of comparatively small factors<ref>{{cite web|url=http://mathworld.wolfram.com/RoundNumber.html|title=MathWorld's definition of a round number|accessdate=3 May 2012}}</ref><ref>Hardy, G. H. (1999). "Round Numbers." Ch. 3 in ''Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work'', 3rd ed. New York: Chelsea, pp. 48–57.</ref> as compared to its neighboring numbers, such as 24 = 2&thinsp;×&thinsp;2&thinsp;×&thinsp;2&thinsp;×&thinsp;3 (4 factors, as opposed to 3 factors for 27; 2 factors for 21, 22, 25, and 26; and 1 factor for 23).

==See also==
*[[Rounding]]
*[[Rounding fraud]]
*[[Significant figures]]
*[[Smooth number]]
*[[Unix billennium]]

==References==
{{reflist}}

[[Category:Numbers]]