A convenient number is a number which in several situations can prove convenient for use by humans for counting and measuring, and is related to
preferred numbers
In industrial design, preferred numbers (also called preferred values or preferred series) are standard guidelines for choosing exact product dimensions within a given set of constraints.
Product developers must choose numerous lengths, distanc ...
(which are
standard Standard may refer to:
Symbols
* Colours, standards and guidons, kinds of military signs
* Standard (emblem), a type of a large symbol or emblem used for identification
Norms, conventions or requirements
* Standard (metrology), an object th ...
recommendations used for choosing
product dimensions).
The convenient numbers in this article were developed in the USA in connection with the attempted introduction of the
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
in the United States in the 1970s. Hence they may be viewed as a recommendation for choosing product dimensions when switching to the metric system, but can also have other uses.
History
In the 1970s, the American
National Bureau of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NBS), which was later renamed to the
National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NIST), defined a set of convenient numbers when it was developing procedures for
metrication in the United States
Metrication (or metrification) is the process of introducing the International System of Units, also known as SI units or the metric system, to replace a jurisdiction's traditional measuring units. U.S. customary units have been defined in t ...
.
An NBS technical note describes that system of convenient metric values as the
1-2-5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10). Linear dimensions above 100 mm were excluded (because such measurements are defined by another set of rules). A table of this 5, 2, 1 series can be seen below in the section "Schedule of convenient numbers between 10 and 100".
The NBS technical note also states that "Basically, integers are more convenient than expressions which include decimal parts
ecimal fractions Furthermore, where measuring devices are used, values which represent numbered subdivisions on such instruments are more useful than values which have to be interpolated. For example, where a tape or a scale is graduated in intervals of 5, any value that represents a multiple of 5 is more "convenient" to measure or verify than one which is not. In addition, where operations involve the subdivision of quantities into two or more equal parts, any number that is highly divisible has an explicit advantage."
Schedule of convenient numbers between 10 and 100
Notes:
# Numbers are shown once only, in the highest applicable preference column. (For example, the number 20 would occur as 3rd, 4th, 5th, and 6th preference as well as 2nd preference).
# In some contexts, 25 and 75 may become 2nd preferences rather than 4th preferences.
The Technical Note also states, "In the practical application of a "convenient numbers approach" to the selection of suitable metric values, it is desirable to start with the highest possible preference and then to gradually refine the difference until an acceptable and convenient metric value has been found."
See also
*
Preferred number
In industrial design, preferred numbers (also called preferred values or preferred series) are standard guidelines for choosing exact product dimensions within a given set of constraints.
Product developers must choose numerous lengths, distance ...
*
Preferred metric sizes
Preferred metric sizes are a set of international standards and de facto standards that are designed to make using the metric system easier and simpler, especially in engineering and construction practices. One of the methods used to arrive at thes ...
*
Idoneal number In mathematics, Leonhard Euler, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers ''D'' such that any integer expressible in only one way as ''x''2 ± ''Dy''2 (where ''x''2 is relativel ...
*
1-2-5 series
*
E-series of preferred numbers
The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
References
{{reflist, refs=
[{{cite web , author-first=Hans J. , author-last=Milton , id=NBS Technical Note 990 (Code: NBTNAE) , title=The Selection of Preferred Metric Values for Design and Construction , date=December 1978 , location=Washington, USA , publisher=]The National Bureau of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NBS) , website=U.S. Government Printing Office , url=https://www.gpo.gov/fdsys/pkg/GOVPUB-C13-f5fea679df4c3a1c2e3e1dd63488707c/pdf/GOVPUB-C13-f5fea679df4c3a1c2e3e1dd63488707c.pdf , access-date=2017-11-01 , url-status=live , archive-url=https://web.archive.org/web/20171101233709/https://www.gpo.gov/fdsys/pkg/GOVPUB-C13-f5fea679df4c3a1c2e3e1dd63488707c/pdf/GOVPUB-C13-f5fea679df4c3a1c2e3e1dd63488707c.pdf , archive-date=2017-11-01
Numbers
Logarithmic scales of measurement
Industrial design