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Ref. No. : lSO/R 17 - 1855 (E)
IS0
INTERN AT1 O NA L ORGAN I2 AT10 N FO R STAN DARD I2 AT1 ON
IS0 RECOMMENDATION
O
R 17
GUIDE TO THE USE OF PREFERRED NUMBERS
AND OF SERIES OF PREFERRED NUMBERS
lst EDITION
April 1956
O
COPYRIGHT RESERVED
The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
a member of ISO.
For each individual country the only valid standard is the national standard of that country.
Printed in Switzerland
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
I 1 1
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BRIEF HISTORY
The IS0 Recommendation R 17 was drawn up by the Technical Committee
ISO/TC 19, Preferred Numbers, the Secretariat of which is held by the Asso-
ciation Française de Normalisation (AFNOR).
At the time when the Committee drew up the IS0 Recommendation R 3,
Preferred Numbers - Series of Preferred Numbers, it appeared necessary to
provide the IS0 Member Bodies with a guide for the use they would be making
of preferred numbers. The work was undertaken in 1949.
Following the Committee’s first meeting, held in Paris in June 1949, the
Secretariat of the Committee drew up two successive draft proposals, the
second of which, distributed in April 1951, was adopted by the Committee, by
correspondence, as a Draft IS0 Recommendation.
The Draft IS0 Recommendation was submitted on 31 October 1951 to
all the IS0 Member Bodies and approved without reserve by 16 Member Bodies.
Nevertheless, in consideration of comments submitted by certain Member
Bodies, the Committee decided, at its second plenary meeting (New York,
June 1952) and its third plenary meeting (The Hague, May 1953), to make some
improvements in the text of the Draft and to add to it a new section No. 5,
giving examples of application, and a section No. 6, relating to the rounding-
off of preferred numbers.
The text of the second Draft IS0 Recommendation (finally revised at
the Committee’s fourth meeting, held in Paris in July 1954) was submitted to
all the IS0 Member Bodies in November 1954 and approved by the following 26
(out of a total of 34) Member Bodies:
Spain
Austria India
Ireland Sweden
Australia
Canada Italy Switzerland
Chile Japan Union of South Africa
Denmark Mexico United Kingdom
Finland Netherlands U.S.A.
U.S.S.R.
France New Zealand
Poland Yugoslavia
Germany
Hungary Portugal
The Secretariat took into consideration certain purely editorial comments
submitted by two Member Bodies, and the Draft, amended accordingly, was
submitted on 31 August 1955 to the IS0 Council, which decided by correspond-
it as an IS0 RECOMMENDATION, subject to certain final
ence to accept
editorial amendments.
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F O R E vC7 O RD
Preferred numbers were first utilized in France at the end of the nineteenth
century. From 1877 to 1879, Captain Charles RENARD, an officer in the
engineer corps, made a rational study of the elements necessary in the construc-
tion of lighter-than-air aircraft. He computed the specifications for cotton rope
according to a grading system, such that this element could be produced in
advance without prejudice to the installations where such rope was subsequently
to be utilized. Recognizing the advantage to be derived from the geometrical
progression, he adopted, as a basis, a rope having a mass of a grammes per
metre, and as a grading system, a rule that would yield a tenth multiple of
the value a after every fifth step of the series, i.e.:
5
a x 45 = IOU or q = 2/10
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whence the following numerical series :
the values of which, to 5 significant figures, are:
a 1.5849 a 2.5119 a 3.9811 a 6.3096a 10a
RENARD’S theory was to substitute for the above values, more rounded
but more practical values, and he adopted as a a power of 10, positive, nil or
negative. He thus obtained the folIowing series :
10 16 25 40 63 100
which may be continued in both directions.
From this series, designated by the symbol R 5, the R 10, R 20, R 40
series were formed, each adopted ratio being the square root of the preced-
ing one:
10 20 40
O
di0 di0 VlO
The first standardization drafts were drawn up on these bases in Germany
Industrie on 13 April 1920, and in
by the Normenausschuss der Deutschen
France by the Commission permanente de standardisation in document X
of 19 December 1921. These two documents offering few differences, the
commission of standardization in the Netherlands proposed their unification.
An agreement was reached in 1931 and in June 1932, the International Feder-
ation of the National Standardizing Associations organized an international
meeting in Milan, where the ISA Technical Committee 32, Preferred Numbers,
was set up and its Secretariat assigned to France.
On 19 September 1934, the ISA Technical Committee 32 held a meeting
in Stockholm ; sixteen nations were represented : Austria, Belgium, Czechoslo-
vakia, Denmark, Finland, France, Germany, Hungary, Italy, Netherlands,
Norway, Poland, Spain, Sweden, Switzerland, U.S.S.R.
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With the exception of the Spanish, Hungarian and Italian delegations
which, although favourable, had not thought fit to give their final agreement,
all the other delegations accepted the draft which was presented. Furthermore,
Japan communicated by letter its approval of the draft as already discussed
in Milan. As a consequence of this, the international recommendation was
laid down in ISA Bulletin 11 (December 1935).
After the Second World War, the work was resumed by ISO. The Technical
Committee ISO/TC 19, Preferred Numbers, was set up and France again held
,
the Secretariat. This Committee at its first meeting, which took place in Paris
in July 1949, recommended the adoption by IS0 of the series of preferred
numbers defined by the table of ISA Bulletin 11, i.e. R 5, R 10, R 20, R 40.
This meeting was attended by representatives of the 19 following nations:
Austria, Belgium, Czechoslovakia, Denmark, Finland, France, Hungary, India,
Israel, Italy, Netherlands, Norway, Poland, Portugal, Sweden, Switzerland,
U.S.A., U.S.S.R.
United Kingdom,
During the subsequent meetings in New York in 1952 and in The Hague
R 80 was added
in 1953, which were attended also by Germany, the series
and slight alterations were made. The draft thus amended has become IS0
Recommendation R 3.
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ISO/RlT - 1- (E)
-
IS0 Recommendation R 17 November 1955
GUIDE TO THE USE OF PREFERRED NUMBERS
AND OF SERIES OF PREFERRED NUMBERS
1. GEOMETRICAL PROGRESSIONS AND PREFERRED NUMBERS
1.1 Standard series of numbers. In all the fields where a scale of numbers
is necessary, standardization consists primarily of grading the charac-
teristics according to one or several series of numbers covering all
the requirements with a minimum of terms.
These series should present certain essential characteristics ; they
0
should :
(a) be simple and easily remembered,
(b) be unlimited, as well towards the lower as towards the higher
numbers,
(c) include all the decimal multiples and sub-multiples of any term,
(d) provide a rational grading system.
1.2 Characteristics of geometrical progressions which include the number I.
The characteristics of these progressions, with a ratio q, are mentioned
below.
I .2.1 The product or quotient of any two terms qb and qc of such
a progression is always a term of that progression:
qb x qc = qb+c
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1.2.2 The integral positive or negative power c of any term qb of such
a progression is always a term of that progression:
(ab)>" = qbc
I
1.2.3 The fractional positive or negative power l/c of a term qb of
such a progression is still a term of that progression, provided
that b/c be an integer:
(@)Il" qb/C
1.2.4 The sum or difference of two terms of such a progression is not
generally equal to a term of that progression. However, there
exists one geometrical progression such that one of its terms
is equal to the sum of the two preceding terms. Its ratio
1 + 2/5
2
approximates 1.6 (it is the Golden Section of the Ancients).
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1.3 Geometrical progressions which include the number 1 and the ratio of
which is a root of 10. The progressions chosen to compute the pre-
ferred numbers have a ratio equal to 310, r being equal to 5, to 10,
to 20, or to 40. The results are given hereunder.
1.3.1 The number 10 and its positive and negative powers are terms
of all the progressions.
1.3.2 Any term whatever of the range lod . lodS1, d being positive
or negative, may be obtained by multiplying by lod the corre-
sponding term of the range 1 . 10.
1.3.3 The terms of these progressions comply in particular with the
property given in clause 1.1, letter (c).
1.4 Rounded off geometrical progressions. The preferred numbers are
the rounded off values of the progressions defined under clause 1.3.
1.4.1 The maximum roundings off are :
+ 1.26% and - 1.01%
The preferred numbers included in the range 1 . 10 are given
in the table of paragraph 1 of IS0 Recommendation R 3,
Preferred Numbers - Series of Preferred Numbers.
1.4.2 Due to the rounding off, the products, quotients and powers
of preferred numbers may be considered as preferred numbers
only if the modes of calculation referred to under section 3
are used.
10
1.4.3 For the R 10 series, it should be noted that 1/10 is equal to
3
d2 at an accuracy closer than 1 in 1000 in relative value, so that :
- the cube of a number of this series is approximately equal
to double the cube of the preceding number. In other words,
the Nth term is approximately double the (N - 3)th term.
Due to the rounding off, it is found that it is usually equal
to exactly the double;
- the square of a number of this series is approximately equal
to 1.6 times the square of the preceding number.
1.4.4 Just as the terms of the R 10 series are doubled in general every
3 terms, the terms of the R 20 series are doubled every 6 terms,
and those of the R40 series are doubled every 12 terms.
1.4.5 Beginning with the R 10 series, the number 3.15, which is nearly
n, can be found among the preferred numbers. It follows
equal to
that the length of a circumference and the area of a circle, the
diameter of which is a preferred number, may also be expressed
by preferred numbers. This applies in particular to peripheral
speeds, cutting speeds, cylindrical areas and volumes, spherical
areas and volumes.
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ISO/R17 - 1955 (E)
I .4.6 The R 40 series of preferred numbers includes the n
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