The legal system of units of measure in force in Spain is, as stated in the second article of Law 3/1985, of March 18, of Metrology, the International System of Units adopted by the General Conference of Pesos and Measures (GFCM) and in force in the European Union. This provision, in the third article, empowers the Government to, by royal decree, establish the definitions of the units, their names and symbols, as well as the rules for the formation of their multiples and submultiples according to the GFCM agreements and European Union legislation.

At the level of the European Union, the regulation is based on Council Directive 80 /181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to units of measurement and the repeals Directive 71 /354/EEC and has been successively amended by Council Directive 85 /11/EEC of 18 December 1984, Council Directive 89 /617/EEC of 27 November 1989, Directive 1999 /103/EC of the European Parliament and of the Council Council Directive of 24 January 2000 and Directive 2009 /3/EC of the European Parliament and of the Council of 11 March 2000 of 2009.

In the context of the agreements of the General Conference of Pesos and Measures the International System of Units (SI) has been successively modified to adapt it to the new needs and technical improvements. The latest version, from 2006, includes a series of new features such as the new definition of the kelvin that includes the detail of the isotopic composition of the triple water point; the consideration of degree Celsius as a unit derived from the temperature thermodynamics; the disappearance of the supplementary units and the consequent consideration of the radian and the stereorradian as units derived from the magnitudes, respectively, of a flat angle and of solid angle; the extension of the prefixes of multiples and submultiples and the acceptance and definition of katal, whose symbol is "kat", as unit of the magnitude of catalytic activity.

The development of Law 3/1985, of March 18, in terms of units of measure, was carried out by Royal Decree 1317/1989, of 27 October, establishing the Legal Units of Measure. This provision was amended years later by Royal Decree 1737/1997 of 20 November.

Directive 2009 /3/EC of the European Parliament and of the Council of 11 March 2009 also sets out the decision of the European Union on the continuity of certain units outside the SI used in certain Member States. prior to 21 April 1973. In the case of the acre, never applied in Spain, the decision is to abolish its use throughout the European Union because it has already been excluded as a measure of the United Kingdom's land registry, in other cases it is extended indefinitely, under the condition of the dual indication, the time limit for its use, which initially expired on 1 January 2010, although the Directive requires the Commission to report on market developments before 31 December 2019.

The successive changes in the three plans-agreements of the General Conference of Pesos and Measures, directives of the European Union and legislation of Spain-make it difficult to draft a legal document with the necessary clarity. (a) by means of a new amendment to Royal Decree 1317/1989 of 27 October 1989. Therefore, it has been decided to draw up a new royal decree that will again systematize and order the various modifications that have been made.

The royal decree consists of a single article and an annex: the single article reproduces the provisions of Law 3/1985, of March 18, on the compulsory use of the International System of Units (SI) adopted by the Conference General of Weights and Measures and in force in the European Union and refers to the annex to relate and define the basic and derived units of the SI, the rules for the formation of multiples and submultiples, the rules of writing of symbols and names of the units and expression of the values of the magnitudes, as well as the use of certain units external to the SI.

This royal decree transposing Directive 2009 /3/EC of the European Parliament and of the Council of 11 March 2009 amending Council Directive 80 /181/EEC on the approximation of the laws of the Member States relating to the approximation of the laws of the Member States members on units of measure.

The project of this royal decree has been favorably informed by the Superior Council of Metrology.

In its virtue, on the proposal of the Minister of Industry, Tourism and Trade, in agreement with the Council of State and after deliberation of the Council of Ministers, at its meeting on 30 December 2009,

DISPONGO:

Single item. Units of measure.

1. The Legal System of Units of Mandatory Measure in Spain is the International System of Units (SI) adopted by the General Conference of Pesos and Measures and in force in the European Union.

2. Related and defined in the Annex to this royal decree the units SI basic (Chapter I), the units SI derived (Chapter II), the rules of writing of the names and symbols of the units and expression of the values of the measures and rules for the formation of multiples and submultiples of such units (Chapter III).

3. The use of the units listed in Chapter IV shall also be authorised, subject to the limitations and in the manner in which they are expressed.

Single additional disposition. Indications of magnitude.

Instruments, apparatus, means and measuring systems shall bear their indications of magnitude in a single unit of legal measure.

Single repeal provision. Regulatory repeal.

Royal Decree 1317/1989, dated October 27, is hereby repealed, establishing the Legal Units of Measure.

Final disposition first. Incorporation of European Union law.

This royal decree incorporates into Spanish law Directive 2009 /3/EC of the European Parliament and of the Council of 11 March 2009 amending Council Directive 80 /181/EEC on the approximation of the laws of the Member States relating to units of measurement.

Final disposition second. Competence title.

This royal decree is issued under the provisions of Article 149.1.12. of the Constitution, which gives the State exclusive competence to dictate the legislation on weights and measures.

Final disposition third. Entry into force.

This royal decree will enter into force the day after its publication in the "Official Gazette of the State".

Given in Madrid, 30 December 2009.

JOHN CARLOS R.

The Minister of Industry, Tourism and Trade,

MIGUEL SEBASTIAN GASCON

ANNEX

CHAPTER I

Basic SI units

1. Enumeration of the basic SI units.

1. The measures referred to and the name and symbol of the basic SI units are as follows:

Table 1

Basic SI Units

Magnitude

Unit name	Drive
Length.	Metro.	m
Masa.
kg Timetable_to_izq"> Time, duration.	Second.	s
stream.	Ampere.	A
thermodynamic temperature.	Kelvin.	K
Quantity of Substance.	Mol.	mol
Intensity.	Candela.

2. Definitions of the basic SI units.

The definitions of the basic SI units are as follows:

2.1 Unit of length (meter, m): The meter is the length of the path taken in the vacuum by the light for a time of 1/299 792 458 of the second.

Here it turns out that the speed of the light in the vacuum is equal to 299 792 458 meters per second exactly, c₀ = 299 792 458 m/s.

2.2 Mass Unit (kilogram, kg): The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram, adopted by the third General Conference of Pesses and Measures in 1901.

2.3 Time Unit (second, s): The second is the duration of 9 192 631 770 radiation periods corresponding to the transition between the two hyperfine levels of the fundamental state of the cesium 133 atom.

Here it turns out that the frequency of the hyperfine transition of the fundamental state of the cesium atom is equal to 9 192 631 770 hercio, ν (hfs Cs) = 9 192 631 770 Hz. This definition refers to a cesium atom at rest, at a temperature of 0 K.

2.4 Electrical current intensity unit (ampere, A): The ampere is the intensity of a constant current which, remaining in two parallel conductors, rectilinear, of infinite length, of negligible circular section and located at a distance of 1 meter from each other, in the vacuum, would produce between these conductors a force equal to 2 × 10^{− 7} newton per meter in length.

Here it turns out that the magnetic constant, μ₀, also known as vacuum permeability, is exactly equal to 4π × 10^{− 7} henriver by meter, μ₀ = 4π × 10^{− 7} H/m.

2.5 Thermodynamic Temperature Unit (kelvin, K): The kelvin, thermodynamic temperature unit, is the 1/273, 16 fraction of the thermodynamic temperature of the triple water point. This definition refers to a water of an isotopic composition defined by the following amount of substance ratios: 0.000 155 76 moles of ²H per mol of ¹H, 0.000 379 9 moles of ¹⁷O per mol of ¹⁶O and 0.002 005 2 moles of ¹⁸O per mol of ¹⁶O.

Here it turns out that the thermodynamic temperature of the triple water point is equal to 273.16 kelvin exactly, T_tpw = 273.16 K.

2.6 Unit of quantity of substance (mol, mol): The mole is the amount of substance in a system that contains as many elemental entities as atoms are in 0.012 kilograms of carbon 12. This definition refers to non-bound, at rest and in its fundamental state, 12 carbon atoms.

When the mole is used, the elementary entities, which may be atoms, molecules, ions, electrons, or other specified particles or groups of such particles, must be specified.

Here it turns out that the molar mass of carbon 12 is equal to 12 g per mol, exactly, M (¹²C) = 12 g/mol.

2.7 Unit of luminous intensity (candela, cd): The candela is the luminous intensity, in a given direction, of a source emitting a monochromatic radiation of frequency 540 × 10¹² hertz and whose energy intensity in that direction of 1/683 watts per stereorradian.

Here it turns out that the spectral luminous efficacy of a monochromatic frequency radiation equal to 540 × 10¹² hertz is equal to 683 lumens per watt, exactly, K= 683 lm/W = 683 cd sr/W.

CHAPTER II

SI-derived units

1. Derived units are formed from products of basic unit powers. Consistent derived units are products of basic unit powers in which no numerical factor is involved more than 1. The basic units and consistent derived units of the SI form a consistent set, called a set of coherent SI units.

2. The number of magnitudes used in the scientific field has no limit; therefore it is not possible to establish a complete list of quantities and derived units. However, table 2 presents some examples of derived magnitudes and corresponding coherent derived units, expressed directly according to the basic units.

Table 2

Examples of consistent derived SI units expressed from the base units

Volume.

			derived magnitude			Consistent Derived SI Unit
Name	Symbol		Name
Area, Surface.	A
V		cubic meter.	m3
.	v		Metro per second.	m/s
	to	Metro per second square.	m/s2
Number of waves.	σ,	~	Metro to power less one.	m-1
		v
Density, mass by volume.	ρ		Kilogram per cubic meter.	kg/m3
Surface Density.	ρA		Kilogram per square meter.	kg/m2
volume.	v		cubic meter per kilogram.	m3/kg
Current Density.	j		Ampere per square meter.	A/m2
field.	H		Ampere per meter.	A/m
of Quantity substance(a), concentration.	c		Mol per cubic meter.	mol/m3
Concentration.	ρ, γ		Kilogram per cubic meter.	kg/m3
v			Lv Table_table_izq"> Candela per square meter.	cd/m2
Refraction Index(b).	N		One.	1
permeability(b).	μr		One.	1

(a) In the field of clinical chemistry, this magnitude is also called concentration of substance.

(b) Are dimensionless magnitudes or dimension one magnitudes. The unit symbol "1" (the number "one") is generally omitted when the value of the dimensionless magnitudes is indicated.

3. For convenience, certain consistent derived units have received special names and symbols. They are listed in Table 3. These special names and symbols may be used with the names and symbols of the basic or derived units to express the units of other derived magnitudes. Examples of this are given in Table 4. Special names and symbols are a compact way of expressing combinations of basic units of frequent use, but in many cases they also serve to remember the magnitude in question. YES prefixes can be used with any of the special names and symbols, but in doing so the resulting drive will not be a consistent unit. The last column of tables 3 and 4 shows how the SI units mentioned according to the basic SI units can be expressed. In this column, the factors in the form m⁰, kg⁰, and so on, which are equal to 1, are not explicitly shown.

Table 3

SI-derived units consistent with special names and symbols

Faradio.

Tesla.

Activity of a radionuclide^(f).

environmental equivalent dose, directional equivalent dose, individual equivalent dose.

	derived magnitude	Consistent Derived SI Unit (a)
		Name	Symbol	Expression using other SI units	Expression in drives YES
Angle.	Radian(b)	rad	(b)	m/m
Angle.	Estereorradian(b).	sr(c)	1(b)	2/m2
Frequency.		-	-1
Force.	Newton.	N	-	m kg s-2
, voltage.	Pascal.	Pa	N/m2	m-1 kg s-2
Energy, work, amount of heat.	July.	J	N m	m2 kg s-2
, energy flow.	Watt.	W	J/s	m2 kg s-3
Electric load, amount of electricity.	Culombian.	C	-	s A
Potential Difference, Electromotive Force.	Volt.	V	W/A	2 kg s-3 to-1
Faradio.		F	C/V	-2 kg-1 s4 A2
Electrical Resistance.	Ohmine.	Ω	V/A	m2 kg s-3 A-2
Siemens.		Siemens.	S	A/V	-2 kg-1 s3 to2
(g)	Weber.	Wb	V s	2 kg s-2 to-1
Tesla.		T	Wb/m2	kg s-2 To-1
	Inductance.		H		m kg s-2 A-2
Celsius Temperature.			-	K
-	-
Flow.	Lumen.	lm	cd sr(c)
Lux.		lx	lm/m2	-2 cd
Becquerel(d)	Bq	-	- -1
Gray.	Gray.	Gy	J/kg	2 s-2
Sy		Sy	Sy	2 s-2
catalytic activity.	Katal.	kat	-	s-1

(a) The SI prefixes can be used with any of the special names and symbols, but in this case the resulting drive is not a consistent unit.

(b) The radian and the stereorradian are special names of the number one, which can be used to provide information regarding the magnitude to which they affect. In practice, the rad and sr symbols are used wherever appropriate, while the symbol of the derived unit "one" is generally not mentioned when you give values of dimensionless magnitudes.

(c) In photometry, the stereorradian name and the sr symbol are generally maintained in the expression of the units.

(d) Hertium is only used for periodic phenomena and becquery for stochastic processes related to the activity of a radionuclide.

(e) Degree Celsius is the special name of the kelvin used to express the temperatures Celsius. The degree Celsius and the kelvin have the same magnitude, so the numerical value of a temperature difference or temperature range is identical when expressed in degrees Celsius or in kelvin. The temperature Celsius t is defined by the difference t = T-T₀, between two thermodynamic temperatures T and T₀, being T₀ = 273,15 K.

(f) The activity of a radionuclide is sometimes called incorrectly radioactivity.

(g) The magnetic flux is also known as magnetic induction flow.

(h) The magnetic flux density is also known as magnetic induction.

Table 4

Examples of consistent derived SI units whose names and symbols contain derived SI units consistent with special names and symbols

kg s

July by kelvin.

Molar Entropy, molar calorific capacity.

A

	derived magnitude	Consistent Derived SI Unit
		Name	Symbol	Expression in drives YES basic
Dynamic viscosity.	Pascal second.	Pa s	-1 kg s
-1kg s-1	Newton metro.	N m	2 kg s-2
per meter		n/m	kg s-2
Angular Speed.	Radian per second.	rad/s	m m-1 s-1 = s-1
Angular Acceleration.	Radian per second square.	rad/s2	m m-1 s-2 = s-2
flow surface density, irradiance.	Watt per square meter.	W/m2
July by kelvin.		J/K	m2 kg s-2 K-1
mm2 kg s m.	July per kilogram and kelvin.	J/ (kg K)	m2 s-2 K-1
Energy.	July per kilogram.	J/kg	m2 s-2
conductivity.	Vatio per meter and kelvin.	W/ (m K)	m kg s-3 K-1
density.	July per cubic meter.	J/m	m-1 kg s-2
Field.	Zc_table_izq"> Voltio per meter.	V/m	m kg s-3 A-1
load density.	Culombian by cubic meter.	C/m3	m-3 s A
load surface density.	Culombian per square meter.		-2 s
flow density, electric offset.	Culombian per square meter.	C/m2	m-2 s A
Faradio by metro.	Faradio per meter.	F/m	m-3 kg-1 s4 To2
permeability.	Henrio per meter.	H/m	m kg s-2 A-2
July by mol.			2 kg s-2 mol-1
July by mol and kelvin.	J/ (mol K)	m2 kg s-2 K-1 mol-1
Exposition (X-rays and γ).	Kg	Kg-1 s A
absorbed dose.	Gray per second.	Gy/s	m2 s-3
Radiant Intensity.	Vatio by stereorradian.	W/sr	m4 m-2 kg s-3 = m2 kg s-3
	W/ (m2 sr)	W/ (m2 sr)	2 m-2 kg s-3 = kg s-3
Kat/m		kat/m	kat/m3	-3 s-1

4. The values of several different magnitudes can be expressed by the same SI unit name and symbol. In this way the July by kelvin is the name of the SI unit for the magnitude thermal capacity as well as for the entropy magnitude. Likewise, the ampere is the name of the SI unit for both the basic intensity of electric current and the magnitude of the magnetomotor force. Therefore it is not enough to use the name of the unit to specify the magnitude. This rule applies not only to scientific and technical texts but also, for example, to measuring instruments (i.e. they must indicate both the unit and the measured magnitude).

5. A derived unit can be expressed in several different ways using basic units and derived units with special names: the July, for example, can be written newton metro or kilogram square meter per second square. This algebraic freedom is in any case limited by physical considerations of common sense and, depending on the circumstances, certain forms may be more useful than others. In practice, to facilitate the distinction between different magnitudes having the same dimension, the use of certain special names of units or combinations of names is preferred. Using this freedom, you can choose expressions that remember how the magnitude is defined. For example, the magnitude moment of a force can be considered as the result of the vector product of a force by a distance, which suggests employing the unit newton meter, the energy per unit of angle advises to use the unit July by radian, etc. The IF frequency unit is the hercio, which involves cycles per second, the SI unit of angular velocity is the radius per second, and the SI unit of activity is the becquerel, which involves accounts per second. Although it would be formally correct to write these three units as second to the power minus one, the use of different names serves to underline the different nature of the measures considered. The fact of using the unit radiates per second to express the angular velocity and the hercio for the frequency, also indicates that the numerical value of the hercio frequency must be multiplied by 2π in order to obtain the numerical value of the speed Corresponding angular in radians per second. In the field of ionising radiation, the SI unit of activity is the becquerel instead of the second elevated to the power minus one, and the SI units of absorbed dose and equivalent dose, respectively, are gray and sievert, instead of July by kg. The special names becquerel, gray and sievert have been specifically introduced to the health hazards that could result from errors in the case that to identify all these magnitudes the units will be used second at least one and July per kilogram.

6. Certain magnitudes are defined by quotient of two magnitudes of the same nature; they are therefore dimensionless, or their dimension can be expressed by number one. The consistent SI unit of all dimensionless magnitudes or dimension one magnitudes is number one, since this unit is the ratio of two identical SI units. The value of these magnitudes is expressed by numbers and the unit "one" is not explicitly mentioned. As an example of such magnitudes, they can be cited, the refractive index, the relative permeability or the coefficient of friction. There are other magnitudes defined as a complex and dimensionless product of simpler magnitudes. For example, among the "characteristic numbers" is the number of Reynolds Re = ρvl/η, where ρ is the density, η the dynamic viscosity, v the velocity and l the length. In all these cases, the unit can be considered as the number one, dimensionless derived unit. Another kind of dimensionless magnitudes are the numbers that represent an account, such as the number of molecules, the degeneration (number of energy levels) or the partition function in statistical thermodynamics (number of accessible states). (a) All of these count measures are considered to be dimensionless or dimension one and have unit SI per unit, even if the unit of the magnitudes that are counted cannot be described as an expressible derived unit in basic units of the SI. For these magnitudes, unit one could be considered as another basic unit. In some cases, however, this unit is given a special name, in order to facilitate the identification of the magnitude in question. This is the case of the radian and the stereorradian. The radian and the stereorradian have received from the GFCM a special name for the coherent derived unit one, in order to express the values of the flat angle and the solid angle, respectively, and consequently appear in Table 3.

CHAPTER III

Rules for writing the symbols and names of the units, expressing the values of the magnitudes, and for the formation of the decimal multiples and submultiples of the SI units

1. Rules for writing the symbols and names of the drives.

1.1 The symbols of the units are printed in Roman characters (straight), regardless of the type of letter used in the adjacent text. They are written in lowercase except if they are derived from a name of their own, in which case the first letter is uppercase. As an exception the use of the letter L in capital or l in lowercase as a litre symbol is allowed to avoid confusion between figure 1 (one) and the letter l (ele).

1.2 A multiple or submultiple prefix, if used, is part of the drive and precedes the drive symbol, with no space between the prefix symbol and the drive symbol. A prefix is never used alone and no compound prefixes are ever used.

1.3 The symbols of the units are mathematical entities and not abbreviations. Therefore, they are not followed by a point, except at the end of a sentence, neither the plural is used, nor can symbols of units with unit names be mixed in the same expression, since the names are not mathematical entities.

1.4 To form the products and ratios of the symbols of the units, the usual rules of multiplication or algebraic division apply. The multiplication must be indicated by a space or a point centered at half height (-), to prevent certain prefixes from being misinterpreted as a symbol of unity. The division is indicated by a horizontal line, an oblique bar (/), or by negative exponents. When combining various symbol units, care must be taken to avoid any ambiguity, for example using brackets or parentheses, or negative exponents. In a given expression without parentheses, no more than one oblique bar should be used, to avoid ambiguities.

1.5 It is not allowed to use abbreviations for the symbols and names of the drives, such as sec (per s or sec), mm cuad. (per mm² or square millimeter), cc (per cm³ or cubic centimeter) or mps (per m/s or meter per second). In this way, ambiguities and misunderstandings are avoided with respect to the values of the magnitudes.

1.6 The names of the units are printed in Roman characters (straight) and are considered common (nouns) names, begin with minuscule (even when their name is that of an eminent scientist and the symbol of the unit) starts by capital, except that they are located at the beginning of a sentence or in a text in capital letters, as a title. To meet this rule, the correct writing of the name of the unit whose symbol is ° C is "degree Celsius" (the degree unit starts with the lowercase g in lowercase and the attribute Celsius starts with the letter C in capital, because it is a name of its own). The names of the drives can be written in plural.

1.7 Although the values of the magnitudes are generally expressed by the names and symbols of the units, if for any reason the name of the unit is more appropriate than its symbol, the name of the unit must be written complete unit.

1.8 When the unit name is combined with the prefix of a multiple or submultiple, no space is left or hyphen is placed between the prefix name and the unit name. The set consisting of the prefix name and the unit name is a single word.

1.9 When the name of a derived unit is formed by multiplication of individual unit names, it is appropriate to leave a space, a point centered at half a height (-), or a hyphen to separate the name of each unit.

2. Write rules to express the values of the measures.

2.1 The value of a magnitude is expressed as the product of a number by a unit: the number that multiplies the unit is the numeric value of the magnitude expressed in that unit. The numerical value of a magnitude depends on the chosen unit. Thus, the value of a particular magnitude is independent of the unit choice, but its numeric value is different for different units.

2.2 The symbols of the magnitudes are generally formed by a single letter in italics, but additional information can be specified through subscripts, superscript, or parenthesis. Thus C is the recommended symbol for calorific capacity, C_m for molar calorific capacity, C_{m, p} for constant pressure molar capacity constant and C_{m, V} for molar-to-volume calorific capacity constant.

2.3 The symbols of the magnitudes are only recommendations, while the correct symbols of the units are required. Where, in particular circumstances, it is preferred to use a symbol not recommended for a given magnitude, for example to avoid confusion resulting from the use of the same symbol for two different magnitudes, it must be clearly stated what it means the symbol.

2.4 The symbols of the units are treated as mathematical entities. When the value of a magnitude is expressed as a product of a numerical value by a unit, the numerical value and the unit can be treated according to the ordinary rules of the algebra. This procedure constitutes the calculation of magnitudes, or algebra of magnitudes. For example, the equation T = 293 K can also be written as T/K = 293.

2.5 Like the symbol of a magnitude does not imply the choice of a particular unit, the symbol of the unit should not be used to provide specific information on the magnitude and should never be the only source of information on the magnitude. Units should not be modified with additional information on the nature of the magnitude; this type of information should accompany the symbol of the magnitude and not the unit.

2.6 The numeric value always precedes the unit and a space between the number and the unit is always left. Thus, the value of a magnitude is the product of a number by a unit, considering the space as a sign of multiplication (same as the space between units). The only exceptions to this rule are the drive symbols of the grade, the minute, and the second flat angle, °, ' and ", respectively, for which no space is left between the numeric value and the unit symbol. This rule implies that the symbol ° C for degree Celsius must be preceded by a space to express the value of the temperature Celsius t.

2.7 In any expression, only one unit is used. An exception to this rule is the expression of the time and flat angle values expressed by units outside the SI. However, for flat angles, it is generally preferable to divide the degree of decimal form. Thus it will be written 22.20 ° better than 22 ° 12 ', except in fields such as navigation, cartography, astronomy, and for the measurement of very small angles.

2.8 The symbol used to separate the entire portion of its decimal part is called the "decimal separator". The decimal separator symbol is the comma, in the write line itself. If the number is between + 1 and -1, the decimal separator is always preceded by a zero.

2.9 Numbers with many figures can be divided into three-digit groups separated by a space, in order to facilitate reading. These groups are never separated by points or commas. In the numbers in a table, the format must not vary in the same column.

2.10 The consistent SI unit of the magnitudes without dimension or dimension one, is number one, symbol 1. The values of these magnitudes are expressed simply by numbers. The unit symbol 1 or the unit name "one" is not explicitly mentioned and there is no particular symbol or special name for the unit one, except for some exceptions that are listed in the tables. As the symbols of the SI prefixes cannot join the symbol 1 or the unit name "one", to express the values of particularly large or particularly small dimensionless magnitudes the powers of 10 are used. In mathematical expressions, the internationally recognized% (percent) symbol can be used with the SI to represent the number 0.01. Therefore, it can be used to express the values of dimension without dimension. When used, it is appropriate to leave a space between the number and the% symbol. When the values of dimensionless magnitudes are expressed in this way, it is preferable to use the% symbol better than the expression "percent". When values of dimensionless fractions are expressed (e.g. mass fraction, volume fraction, relative uncertainty, etc.), it is sometimes useful to use the ratio between two units of the same type. The term "ppm" meaning 10⁶ in relative value or 1 x 10^-6 or "parts per million" or millionths, is also used. When any of the terms%, ppm, etc. are used, it is important to declare what is the magnitude without dimension whose value is being specified.

3. Rules for the formation of the decimal multiples and submultiples of the SI units.

3.1 The decimal multiples and submultiples of the SI units are formed by prefixes that designate the decimal numeric factors by which the unit is multiplied and listed in the "factor" column of Table 5.

Table 5

YES Prefixes

Prefixes IF^(a)

10^-1

c

⁶

⁹

Giga.

10²⁴

Factor	Name	Symbol	Factor	Name
101	Deca.	Deca.		-1			d
2	h		10-2	102
k	k	10-3	m
Mega.	m		-6 10-6		μ
Giga.		G	10	Nano.	n
	Tera.	12	T		p	p
15	P		10-15 10-15
18	Exa.	E	10-18	to
21	Zetta.	to	to	Z	10-21	z
Yotta.	and	10-24	and
and

(a) The SI prefixes represent strictly powers of 10. They should not be used to express powers of 2 (for example, a kilobit represents 1000 bits and not 1024 bits). The prefixes adopted for binary powers do not belong to the SI. The names and symbols used for prefixes for 2¹⁰, 2²⁰, 2³⁰, 2⁴⁰, 2⁵⁰ , and 2⁶⁰ are, respectively, kibi, Ki; mebi, Mi; gibi, Gi; tebi, Ti; pebi, Pi; and exbi, Ei. Thus, for example, a kibibyte is written: 1 KiB = 2¹⁰ B = 1024 B. These prefixes can be used in the field of information technology to avoid incorrect use of SI prefixes.

3.2 The symbols of the prefixes are written in Roman characters (straight), such as the symbols of the units, regardless of the letter type of the adjacent text, and join the symbols of the units, leaving no space between the prefix and the drive symbol. With the exception of da (deca), h (hecto), and k (kilo), all multiples prefix symbols are written with uppercase and all submultiples prefix symbols are written with lowercase. All prefix names are written with lowercase, except at the beginning of a sentence.

3.3 The group consisting of a prefix symbol and a unit symbol constitutes a new inseparable unit symbol (forming a multiple or a submultiple of the unit in question) that can be elevated to a positive power or negative and can be combined with other composite unit symbols.

Examples:

2.3 cm³ = 2.3 (cm)³ = 2.3 (10^-2 m)³ = 2,3 × 10^-6 m³.

1 cm^-1 = 1 (cm)^-1 = 1 (10^-2 m)^-1 = 10² m^-1 = 100 m^{− 1}.

1 V/cm = (1 V)/(10^-2 m) = 10² V/m = 100 V/m.

5000 µ s^{− 1} = 5000 (µ s)^{− 1} = 5000 (10^{− 6} s)^{− 1} = 5 × 10⁹ s^{− 1}.

3.4 Prefix names are inseparable from the names of the units to which they are joined. Thus, for example, millimeter, micropascal and meganewton are written in a single word. The symbols of compound prefixes; that is, the symbols of prefixes formed by juxtaposition of two or more prefix symbols, are not allowed, for example should be written nm (nanometer) and not m µ m. This rule also applies to the names of the compound prefixes. The symbols of the prefixes cannot be used alone or joined to the number 1, symbol of the unit one. Similarly, the names of the prefixes cannot join the name of the unit one, that is, the word "one".

3.5 Prefix names and symbols are used with some units outside the SI, but they are never used with units of time: minute, min; hour, h; day, d. Astronomers use the arc (or grade) millisecond, "plus" symbol, and the arc microsecond, symbol "μas," as units of measure of very small angles.

3.6 Among the basic units of the International System, the unit of mass is the only one whose name, for historical reasons, contains a prefix. The names and symbols of the multiples and decimal submultiples of the mass unit are formed by adding the names of the prefixes to the word "gram" and the symbols of these prefixes to the "g" unit symbol.

CHAPTER IV

Other units

1. Table 6 includes non-SI units whose use with the International System is accepted, since they are widely used in everyday life and each has an exact definition in SI units. Includes traditional time and angle units. It also contains the hectare, the litre and the tonne, which are all commonly used worldwide, and which differ from the corresponding SI units corresponding in a factor equal to an entire power of ten. YES prefixes are used with multiple of these drives, but not with the time units.

Table 6

Non-SI units whose use is accepted by the System and are authorized

Magnitude

Angle.

Unit name	Symbol	Value in units
Time.	Minute.	min	1 min = 60 s
	Time.	h	1 h = 60 min = 3600
Day.	d	1 d = 24 h = 86 400 s
Grade (a, b).		1º = (π/180) rad
Minute.	'	1' = (1 /60) º = (π/ 10 800) rad
Second (c)	"	1" = (1/60) ' = (π/ 648 000) rad
Area.	ha		ha	ha Centro_table_body "> 1 ha = 1 hm2 = 104 m2
Volume.	Litro (d).	L, l	1 L = 1 l = 1 dm3 = 103 cm3 = 10-3 m3
.	Ton.	t	1 t = 103

(a) It is recommended that the degree be divided into decimal form, rather than using the minute and the second. However, for navigation and topography, the advantage of using the minute lies in the fact that one minute of latitude on the Earth's surface corresponds (approximately) to a nautical mile.

(b) The gon (or centesimal grade, where centesimal grade is the alternative name of gon) is an angle-angle unit alternative to grade, defined as (π/200) rad. A straight angle corresponds to 100 gon. The potential value of the gon in navigation is that the distance between the Pole and the Equator of the Earth is equal to about 10 000 km; 1 km on the surface of the Earth subtends as an angle of a centigon from the center of the Earth. The gon is in any case rarely used (if used in the handling of theodolites and total stations, in topographic and civil engineering applications).

(c) In astronomy, small angles are measured in arc seconds (i.e., flat-angle seconds), mili-, micro or arcing picoseconds (symbols: as or, " plus, μas and pas, respectively). The second arc or the second degree are other names in the second plane angle.

(d) The two lowercase "l" and capital "L" symbols are usable for the liter unit. The use of the capital 'L' is recommended to avoid the risk of confusion between the letter l (ele) and the figure 1 (one).

2. The units in Table 7 are linked to the fundamental constants and their value in SI units is determined experimentally and therefore have an associated uncertainty. With the exception of the astronomical unit, all the units of the table are linked to fundamental constants of physics. The use with the SI of the first three units of the table is accepted: the electronic volt, symbol eV, the dalton or unified atomic mass unit, symbol Da or u, and the astronomical unit, symbol au.

3. The two most important unit systems based on the fundamental constants are: the system of natural units (u. n.), used in the field of the physics of high energies and particles, and the system of atomic units (u. a.), used in atomic physics and in quantum chemistry. Table 7 shows the experimentally obtained value in SI units. Since the systems of magnitudes on which these units are based differ in a fundamental way from the IF they are not used with it. The final result of a measure or a calculation expressed in natural or atomic units must also always be indicated in the corresponding SI unit. Natural units (u. n.) and atomic units (u. a.) are used only in the particular fields of particle physics, atomic physics and quantum chemistry. The typical uncertainties of the last significant figures are enclosed in parentheses after each numeric value.

Table 7

Non-SI units whose value in SI units is obtained experimentally

Magnitude

Action (reduced plankton constant).

Time.

Unit name	Symbol	Value in units SI (a)
Units used with the
Energy.	(b	eV	eV	1 eV = 1,602 176 487 (40) × 10-19
.	(c).	Da	1 Da = 1,660 538 782 (83) × 10-27
	Unified Atomic Mass Unit	u	1 u = 1 Da
.	Astronomical Unit(d)	ua	1 ua = 1,495 978 706 91 (6) × 1011
Units or. n.
(speed of light in the vacuum).	Natural speed unit.	c0	299 792 458 m/s (exact
Natural Action Unit		1,054 571 628 (53) × 10-34 J s
(electron mass).	Mass natural unit.		9,109 382 15 (45) × 10-31
Time.	Table_table_izq"> Natural time unit.	ħ/ (mec02)	1,288 088 6570 (18) × 10-21
atomic units or. a.
(elementary electrical charge).	Atomic load unit.	e	1,602 176 487 (40) × 10-19
(electron mass).	Mass atomic unit.	m	9,109 382 15 (45) × 10-31
Action (reduced Planck constant).	Atomic action unit.		1,054 571 628 (53) × 10-34 J
	Length, bohr (Bohr radio).		to0		to0 Centro_table_body"> 0.529 177 208 59 (36) × 10-10
, hartree (Hartree energy).	Atomic power unit.	Eh	4,359 743 94 (22) × 10-18
Time.	Time Atomic Unit	ħ/Eh	2,418 884 326 505 (16) × 10-17

(a) The values in SI units of all the units in the table, except the astronomical unit, are derived from the ratio of core constant values recommended by CODATA (2006). The typical uncertainty referred to in the last two figures is indicated in brackets. The values provided are reviewed periodically.

(b) Electronvolt is the kinetic energy acquired by an electron after crossing a potential difference of 1V in the vacuum. Electronic volt is often combined with SI prefixes.

(c) The dalton (Da) and the unified atomic mass unit (u) are other names (and symbols) for the same unit, equal to 1/12 of the mass of the free ¹²C atom, at rest and in its fundamental state. Dalton is often combined with SI prefixes, for example to express the mass of large molecules in kilodaltons, kDa or megadaltons, MDa and to express the value of small mass differences of atoms or molecules in nanodaltons, nDa, and even in picodaltons, pDa.

(d) The astronomical unit is approximately equal to the average distance between the Sun and the Earth. It is the radius of a circular newtonian orbit not disturbed around the Sun, of an infinitesimal mass particle, moving at an average speed of 0.017 202 098 95 radians per day (also called Gauss constant).

4. Table 8 contains non-SI units used to respond to specific needs of certain groups. Those who use the units in Table 8 should always indicate their definition in SI units. Table 8 also cites the units of the logistic magnitudes, the nester, the belium and the decibel. These are dimensionless units and are used to provide information on the logarithmic nature of the magnitudes ratio. The nep, Np, is used to express the value of the neperiane (or natural) logarithms of relationships between magnitudes, ln = loge. The belium and decibel, B and dB, 1 dB = (1/10) B, are used to express the value of base 10 logarithms between magnitudes, lg = log10. The Nepalese, belium and decibel units are accepted for use with the SI but are not considered SI units. The SI prefixes are used with two of the units in Table 8, namely with the bar (e.g. milibar, mbar) and with the belium, in particular decibel, dB. The table is explicitly mentioned in the decibel, since the war is rarely used without this prefix.

Table 8

Other non-SI units of exclusive application in specific sectors

Magnitude

Unit name	Symbol	Value in SI units
.	Bar(a	bar	1 bar = 0.1 MPa = 100 kPa = 105
		mmHg
Length.	Angstrom(c)	A	1 A = 0.1 nm = 100 pm = 10-10
Distance.	Mile nautical(d)	M	1 M = 1852 m
Surface.	Barn(e	b	1 b = 100 fm2 = (10-12 cm)2 = 10-28 m2
Speed.	(f	kn	1 kn = (1852/3600) m/s
Np	Np		[see the note (j) with respect to the numeric value of the nep, the belium and the decibel.]
	(h, i)	B
		Decibel(h, i)		dB
of optical systems.	Dioptria(k).	-	1 dioptria = 1 m-1
	1 quilate	-	- metric = 2-10-4
Area or surface of farm and farm surfaces.	Area(k).	to	1 to = 102 m2
longitudinal mass of textile fibers and threads.	Tex(k).	tex	1 tex = 10-6 kg-m-1
Angle.	Return(k)	-	1 return = 2π rad

(a) All thermodynamic data refers to the normal pressure of a bar. Before 1982, normal pressure was the normal atmosphere, equal to 1,013 25 bar or 101 325 Pa.

(b) The millimeter of mercury is used only for the measurement of blood pressure and other body fluids.

(c) The angstrom is widely used in X-ray crystallography and in structural chemistry because all chemical bonds are in the range of 1 to 3 angstroms.

(d) The nautical mile is a unit used in sea and air navigation to express distances There is no internationally agreed symbol, but the symbols M, NM, Nm and nmi are used; in Table 8 only the symbol M. unity was established at its origin, and still continues to be used, because a nautical mile on the surface of the Earth subtends approximately one minute of angle from the center of the Earth, which is convenient when measuring latitude and the length in degrees and minutes of angle.

(e) The barn is a surface unit used in nuclear physics to characterize effective sections.

(f) The knot is defined as a nautical mile per hour. There is no internationally agreed symbol, but the kn symbol is usually used.

(g) The equality L_A = n Np (where n is a number) must be interpreted with the meaning ln (A₂/A₁) = n. So When L_A = 1 Np, A₂/A₁ = e. Symbol A is used here to designate the amplitude of a senoidal signal and L_A as the neperiane logarithm of a ratio of amplitudes or neperiana difference of a level of amplitudes.

(h) The equal L_X = m dB = (m/10) B (where m is a number) must be interpreted with the meaning lg (X/X₀) = m/10. So when L_X = 1 B, X/X₀ = 10 and when L_X = 1 dB, X/X₀ = 10^1/10. If X represents a mean quadratic signal or a potential type magnitude, L_X is called the power level X₀.

(i) When using these units, it is important to indicate the nature of the magnitude in question and the reference value used. These units are not SI units, but their use is accepted with the SI.

(j) It is not usually necessary to specify the numerical values of the nester, the belium and the decibel (neither the relation of the belium and the decibel to the nep). This depends on how the logarithmic magnitudes are defined.

(k) This unit is not collected in the documents adopted by the General Conference of Weights and Measures.