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Expressing SI Units

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Expressing SI Units Chapter 7 Expressing SI Units 7.1 Introduction We have discussed about the evolution of the International System of Units, base units, coherent derived units and non-SI units in the last few chapters. Continuing the subject, in this chapter we are going to discuss about SI prefixes, their use, and methods to express the quantities with proper numerals and units. The specific advantage of the International System of Units (SI) will also be discussed. 7.2 SI Prefixes The 11th CGPM (1960) [1] adopted a series of prefixes and their symbols to form the names and symbols of the decimal multiples and submultiples of SI units ranging from 1012 to 1012. Prefixes for 1015 and 1018 were added by the 12th CGPM (1964) [2], for 1015 and 1018 by the 15th CGPM (1975) [3, 4] and for 1021, 1024, 1021 and 1024 by the 19th CGPM (1991) [5, 6]. All prefixes and their respective symbols, approved till date, are given in Table 7.1. These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (e.g. one kilobit represents 1,000 bits and not 1,024 bits). 7.2.1 Rules for Using SI Prefixes In accordance with the general principles adopted by the ISO (ISO 31), the CIPM recommended that the following rules be observed when using SI prefixes: 1. Regardless of the type used in the surrounding text, all prefix symbols are printed in roman (upright) type and are attached to unit symbols with no space between the prefix symbol and the unit symbol. 2. Similarly prefix names are also inseparable from the unit names to which they are attached. Thus, for example, millimetre, micropascal and meganewton are single words. 95 96 7 Expressing SI Units Table 7.1 SI prefixes Factor Name Symbol Factor Name Symbol 1024 Yotta Y 101 Deci d 1021 Zetta Z 102 Centi c 1018 Exa E 103 Milli m 1015 Peta P 106 Micro 1012 Tera T 109 Nano n 109 Giga G 1012 Pico p 106 Mega M 1015 Femto f 103 Kilo k 1018 Atto a 102 Hecto ha 1021 Zepto z 101 Deca da 1024 Yocto y 3. With the exception of da (deca), h (hecto) and k (kilo), all multiple prefix symbols are in capital (upper case) letters, and all submultiple prefix symbols are in lower case letters. 4. All prefix names are printed in lower case letters, except at the beginning of a sentence. 5. The grouping formed by the prefix symbol attached to the unit symbol constitutes a new inseparable symbol (of a multiple or submultiple of the unit concerned), which can be raised to a positive or negative power and combined with other unit symbols to form compound unit symbols. For example: 1 cm3 D 102 m3 D 106 m3 1s1 D 106 s1 D 106 s1 1 Vcm1 D 1 V 102 m1 D 102 Vm1 1 cm1 D 102 m1 D 102 m1 6. Compound prefixes, i.e. prefixes formed by the juxtaposition of two or more SI prefixes, are not permitted. This rule also applies to compound prefix names. Do not write nm as 1 mm. Similarly microcentimetre with symbol cm is also not allowed. 7. Prefix symbols can neither stand-alone nor be attached to the number 1, the sym- bol for the unit one. Similarly, prefix names cannot be attached to the name of the unit one, i.e. to the word ‘one’. We cannot say mega men for one million men. 8. Prefix names and symbols are used with a number of non-SI units, but they are never used with the units of time like minute (min), hour (h) and day (d). How- ever, astronomers use milliarcsecond, which they denote as mas, and microarc- second, denoted as as, which they use as units for measuring very small angles. 7.3 Writing of SI Unit Symbols 97 7.2.2 Prefix About the Kilogram Among the base units of the International System, the kilogram is the only one whose name and symbol, for historical reasons, include a prefix. Names and sym- bols for decimal multiples and submultiples of the unit of mass are, therefore, formed by attaching prefix names to the unit name ‘gram’, and prefix symbols to the unit symbol ‘g’ [7, 8]. 7.3 Writing of SI Unit Symbols 7.3.1 Unit Symbols and Their Combinations 1. Every symbol of a unit is written in roman upright form. In general, unit symbols are written in lower case, but, if the name of the unit is derived from the proper name of a person, the first letter of the symbol is a capital. When the name of a unit is expressed in full, it is always written in lower case, except for the term ‘degree Celsius’ or when a sentence starts with the name of the unit. 2. The 16th CGPM (1979), Resolution 6, permitted the use of either capital L or lower case l for the litre. This was done in order to avoid possible confusion between the numeral 1 (one) and the lower case letter l (el). 3. A multiple or submultiple prefix, if used, is part of the unit and precedes the unit symbol without a separator. A prefix is never used in isolation, and compound prefixes are never used. 4. Unit symbols are mathematical entities and not abbreviations. Therefore, they are not followed by a period except at the end of a sentence. For example, one may write a rod is 5.6 cm long, not a rod is 5.6 cm. long 5. Unit symbols are not to be changed in the plural. For example, one should write 100 kg, not 100 kgs. 6. Unit symbols and unit names are not to be mixed within one expression, since names are not mathematical entities. 3 For example, for writing the unit of mass density use either kgm3,kg=m or kilogram per metre cube but not kilogram per m3 or kg per metre cube. 7. In forming products and quotients of unit symbols the normal rules of algebraic multiplication or division apply. Multiplication must be indicated by a space or a middle dot (), since otherwise some prefixes could be misinterpreted as a unit symbol. Indicate division by a horizontal line, a solidus (oblique stroke,/) or negative exponents. When several unit symbols are combined, care should be taken to avoid ambiguities, e.g. by using brackets or negative exponents. A solidus must not be used more than once in a given expression without brackets to remove ambiguities. 98 7 Expressing SI Units For example, one may write m/s or ms1 for metre per second Write ms for millisecond and m s for metre times second the same may be written as m s. Expressions like m kg/(s3A), or m kg s3 A1 are permitted but not 3 3 m kg=s =A, or m kg=s A. Work done in joules is expressed as m2 kg s2 and permeability as m kg s2A2; these are some examples for expressing quantities involving many units. 8. It is not permissible to use abbreviations for unit symbols or unit names, such as: sec for either s or second 2 sq. mm for either mm or square millimetre 3 cc for either cm or cubic centimetre mps for either m/s or metre per second The use of the correct symbols for SI units, and for units in general, as listed in the book, is mandatory. In this way ambiguities and misunderstandings in the values of quantities are avoided. 7.3.2 Names of Units 1. Unit names are normally printed in roman (upright) type, and are treated like ordinary nouns. In English, the names of units start with a lower case letter (even when the symbol for the unit begins with a capital letter), except at the beginning of a sentence or in capitalized material such as a title. In keeping with this rule, the correct spelling of the name of the unit with the symbol ıC is ‘degree Celsius’ (the unit degree begins with a lower case d and the modifier Celsius begins with an upper case C because it is a proper name). Other examples are joule symbol (J); hertz symbol (Hz); second symbol (s), ampere symbol (A) and watt (W). 2. Although the values of quantities are normally expressed using symbols for num- bers and symbols for units, if for some reason the unit name is more appropriate than the unit symbol, the unit name should be spelled out in full. For example, we may write 5.9 N or 5.9 newtons; no abbreviation for the name of the unit can be used. 3. When the name of a unit is combined with the name of a multiple or submultiple prefix, no space or hyphen is used between the prefix name and the unit name. The combination of prefix name plus unit name is a single word; e.g. millimetre and not milli-metre. One should write kilopascal rather than kilo-pascal. 4. In both English and French, however, when the name of a derived unit is formed from the names of individual units by multiplication, either a space or a hyphen is used to separate the names of the individual units. 7.3 Writing of SI Unit Symbols 99 5. In both English and French, qualifiers such as ‘squared’ or ‘cubed’ are used in the names of units raised to powers, and they are placed after the unit name. However, in the case of area or volume, as an alternative the qualifiers ‘square’ or ‘cubic’ may be used, and these modifiers are placed before the unit name, but this applies only in English.
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