Convenient number

The concept of convenient numbers is related to that of preferred numbers. A structure is defined to build a set of numbers that are convenient for use by humans in counting or measuring.

National Bureau of Standards (NBS) (which was later renamed to the National Institute of Standards and Technology (NIST)) defined a set of convenient numbers during the 1970s when it was developing procedures for metrication in the United States. The 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), excluding linear dimensions above 100 mm (because such measurements are defined by another set of rules), from which the Schedule of Convenient Numbers Between 10 and 100 below is reproduced.[1]

The NBS technical note also states that "Basically, integers are more convenient than expressions which include decimal parts [decimal 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

1st preference n × 50	2nd preference n × 20	3rd preference n × 10	4th preference n × 5	5th preference n × 2	6th preference n × 1
		10
					11
				12
					13
				14
			15
				16
					17
				18
					19
	20
					21
				22
					23
				24
			25*
				26
					27
				28
					29
		30
					31
				32
					33
				34
			35
				36
					37
				38
					39
	40
					41
				42
					43
				44
			45
				46
					47
				48
					49
50
					51
				52
					53
				54
			55
				56
					57
				58
					59
	60
					61
				62
					63
				64
			65
				66
					67
				68
					69
		70
					71
				72
					73
				74
			75*
				76
					77
				78
					79
	80
					81
				82
					83
				84
			85
				86
					87
				88
					89
		90
					91
				92
					93
				94
			95
				96
					97
				98
					99
100

Notes:

1. 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).
2. 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
• Preferred metric sizes
• Idoneal number
• 1-2-5 series
• E-series of preferred numbers

References

1. Milton, Hans J. (December 1978). "The Selection of Preferred Metric Values for Design and Construction" (PDF). U.S. Government Printing Office. Washington, USA: The National Bureau of Standards (NBS). NBS Technical Note 990 (Code: NBTNAE). Archived (PDF) from the original on 2017-11-01. Retrieved 2017-11-01.