Units of measurement: representation and writing rules



Over the course of my career as a designer of electrical systems and technical manager of various companies, I have often heard, especially from the experts; The mains voltage is 220 volts, or you receive documents with units of measurement incorrectly written, incomplete and sometimes even completely incomprehensible.

It is good to remember that using incorrectly the names and symbols of the units of measure and the prefixes, is equivalent to making serious misspellings, that especially in the field of electrical and electronic systems design, can transfer an information Completely different from what was intended to provide, with even risks of damage to those who receive it and interpret it according to what was wrongly written.

In order to clarify some of the ideas it is good to clarify some fundamental concepts of the units of measure, of their representation and above all of their correct writing.

Basic concepts

A certain procedure is defined as a measure whereby a number is matched to a physical magnitude.

In order to measure a magnitude, it is necessary to choose another of the same species to be used as sample and to assign to it the numerical value one, thus defining the unit of measure. The units of measurement defined directly by a sample, are called “fundamental units” and those that use one or more samples of the fundamental units are called “derived units“. For example, providing information F = 50 is a wrong expression, even if it is inserted in an intuitive context, correct information must always be represented by a dimensional equation, so the correct expression is F = 50 Hz, where F represents The symbol of magnitude, in this case the frequency, 50 is a pure number representing the value and Hz represents the unit of measure. The units of measurement are represented by a symbol and are encoded according to the international system of units of measure (Systeme International d’denominations) conventionally abbreviated to SI, a system introduced in 1960 by the eleventh General Conference of Weights and measurements, replacing the old CGS systems (centimeter, gram, second) and MKS (meter, kilogram, second). .

The international system of units of measure

In Italy The SI was adopted as a mandatory legal system with the DPR no 802 of 12 August 1982 “Implementation of the EEC Directive 80/181 on the units of measure” and, subsequently adapted to the EC directive 2009/3 of 11 March 2009, by decree of Ministry of Economic Development on 29 October 2009, and entered definitively in force on 1 January 2010.

The DM of 29 October 2009, through the adoption of the SI, dictates the rules of writing and establishes the symbols and their use, in order to provide a uniform and shared way for the measures in all the Member States of the European Union, for these reasons the rules of the SI are one That give certainty of non-ambiguity and non-contestability in the national and international field. The SI is the subject of directives of the European Community and the dissemination and control, in our country, are entrusted to UNI, while the supervision of the application of DPR 802/82 and subsequent decree of 29 October 2009, is entrusted To the Ministry of Industry, Commerce and crafts through the metric central Office and the metric provincial offices.

The task of the metric office is to ensure that the correct use of the fundamental and derived units of measurement as prescribed by the norms is made, in the context not only of the economic activities but also of those of administrative nature and Legal. The SI is based on seven fundamental units and is known as “metric system”, where the metric word derives from the Greek measure and the decimal word refers to the basis of the system of relationship between the measures that are multiple or subultiple of the ten.

The seven fundamental units are:

  • Meter (m), is the length of the journey path from the light in the vacuum in a range of 1/299 792 458 seconds;
  • Second (s), is the duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the fundamental state of the cesium Atom 133;
  • Kilogram (kg), is the mass unit; It is equal to the mass of the international prototype of the kilogram ≫ prototype made of Iridium Platinum in 1889 and conserved in Sevres;
  • Amperes (a), is the intensity of a constant electric current which, kept in two parallel straight conductors of infinite length, of negligible circular section, placed at the distance of one meter from each other in the void, would produce between these conductors A force equal to 2 x 10-7 Newton on each metre of length;
  • Kelvin (K), thermodynamic temperature unit, is the fraction 1/273,16 of the thermodynamic temperature of the triple point of the water;
  • Mole (MOL), is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon 12. When using the mole, the elementary entities must be specified; They can be atoms, molecules, ions, electrons, other particles, or specified groupings of such particles;
  • Candle (CD), is the luminous intensity, in a given direction, of a source emitting a monochromatic frequency radiation 540×1012 Hertz and whose energy intensity in that direction is 1/683 watts to the Steradian.
Fig. 1: The 7 fundamental units

Are some of the derived magnitudes of SI:

  • area, the unit of measure adopted is the square metre (m2);
  • Volume, the unit of measure adopted is the cubic metre (m3);
  • Speed, the unit of measure is the meter per second (m/s);
  • Acceleration, the unit of measure is the meter per second square (m/s2);
  • Electric current density, the unit of measurement is amperes per square metre (A/m2);
  • electric field intensity, the unit of measurement is volt per metre (V/m);
  • Electrical resistivity, the unit of measurement is ohm per metre (Ω · m).
Fig. 2: Diagram of relations between SI units (from NIST)

Often the designer, especially in electronics, is to have to represent very large or very small quantities compared to the units of measurement, in these cases the is recommended to use a prefix that multiplies (multiple) or divides (submultifold) the unit of Measure. The following are the prefixes of subcultures and multiples authorized by the SI, note that the subultipli of the unit of measure must be written in lowercase letters, while the multiples of the measure units must be written with uppercase letters to exception of Kilo (k):

Submultiples Multiple
Prefix Symbol Name Prefix Symbol Name
10-18 in Act 1018 And Exa
10-15 f Femto 1015 P Peta
10-12 p Pico 1012 T Tera
10-9 n Nano 109 G Giga
10-6 Μ Micro 106 M Mega
10-3 m Milli 103 k Kilo

If the representation of an information characterized by a certain approximation is to be used, by convention it can be explicitly indicated, i.e. bringing the most probable value followed by the value of uncertainty as a variation in More or less, for example F = 50 ± 0.5 Hz indicates a frequency whose value can be between 49.5 and 50.5 Hz. There is no general convention for the symbols to be used for the magnitudes, except for the fundamental and derived units, they depend very much on the context in which they are used, it is still good practice to follow the following general rules:

  • Choose for a given size a symbol that does not cause ambiguity with other symbols chosen for other sizes or with the symbols of the units of measure;
  • Once you have chosen a symbol for a magnitude it must not be changed in the same context.

From 1 January 2010 following the DM of 29 October 2009, the following quantities are no longer legally permissible:

  • Quintal (q) replaced by 100 kg;
  • Atmosphere (ATM) replaced by 101,325 Pa;
  • Horse Steam (CV) replaced by 735.499 W;
  • Calorie (CAL) replaced by 4.1868 J;
  • Kilogram-Force (KGF) replaced by 9.80665 N.

Some rules

For the purposes of a correct interpretation of the information relating to the design requirements, the correct writing of the names and symbols of the physical quantities is of paramount importance to the designer. The following are the most important rules of the SI concerning the writing of the quantities, names and symbols of the units; They are valid in general, that is also for units that do not belong to the SI:

-The IS established as a unit of temperature measurement the Kelvin (K) and the degree Celsius (°c), therefore a temperature can be expressed both in Kelvin and in degrees Celsius, the relationship that binds the two values is as follows: temperature in degrees Celsius (t) = temperature in K Elvin (T) – 273.15. The temperature unit is called Kelvin not Kelvin grade, while the symbol °c refers to the degree Celsius and no longer to the degree centigrade that has now been abandoned;

-In the case of numerical expressions, the symbols of the units of measure must be written in normal character, while the symbols of the sizes can be written in italic character. In particular those constants in time are indicated with symbols italic uppercase, while those variables over time are indicated with lowercase cursive symbols. In this way it avoids confusion when the same letter is used both for the magnitude and for its unit of measure, for example by writing: V (italics) = 12 V is understood unequivocally, that it is a continuous voltage of the value of twelve Volts , instead if you write: V (italic) = 12 V is unequivocally understood, that it is an alternating voltage of twelve volts, so that the incomprehensible abbreviates must not be used: D.C., AC, DC, AC, DC, CA, etc;

-The names of the units of measure must always be written with the initial lowercase letter, without accents or other graphical signs, except when the name is the first word of a sentence, except for the degree Celsius unit;

-The names of the units of measure, if they derive from a proper name, are unchanged in the plural;

-The unit of measurement if not accompanied by the numerical value, shall be written in full and not with the symbol, except for drawings, elevations, etc.;

-in numerical processing, to avoid errors, it is recommended the use of the SI units and not of their multiples or subversions, however to express the data of numerical elaborations or of measurements where the significant figures are few, it is possible to use that its Multiple or submultiples that give rise to numeric values that only include significant digits. For example, instead of writing 0.00282 m it is preferable to write 2.82 mm; Instead of writing 0.000348 m3 it is preferable to write 348 mm3; Instead of writing 2 000 000 Hz it is preferable to write 2 GHz; Instead of writing 0.0035 A is preferable to write 3.5 but. It may be derogated from this recommendation when it is considered necessary to use, in a given context, a single measure of measurement in order to avoid any ambiguity and misunderstandings;

-Symbols must always be written with the initial lowercase letter, except those deriving from proper names;

-The symbol must not be followed by a point unless it is at the end of the period;

-The symbol must always follow the numerical value;

-the symbol of the multiple or sub-multifold must precede the unit of measure symbol without the interposing of a point or a space;

-The prefix kilo (k) must be lowercase, the capital letter K indicates the temperature in Kelvin;

-the product of two or more units should be indicated with a point at half height or with a small space between the symbols;

-The product of a unit for itself n times, must be indicated with a power of unity and not with abbreviations for example m2 not MQ or MQ or M3 non MC or MC;

-the quotient between two units should be indicated with a slash or negative exponents;

-The hour, minute, second symbols shall be h, Min, S, respectively;

-Monetary symbols precede the number to which they refer;

-the separation between integers and decimals must be made using the comma (the point for the English text is allowed), either to the left of the comma (whole part), or to the right of the comma, the numbers can be grouped in groups of three digits Separated by a space slightly higher than the space between the digits, the grouped numbers can never be separated by points;

-The elements constituting a date in purely numerical form must be written in the following order: year (4 digits) – month (2 digits) – Day (2 digits);

-The coefficients (number of atoms in the molecule) in the symbols of the chemical compounds, are written in the lower right of the symbol of the element to which they refer;

-Between a number and a power of 10, only one half-height point should be inserted, while between the literal symbols it is possible to insert either a half-height point or a space.

Some examples of units of measure representation:

Correct Wrong
230 V-Two hundred and thirty Volts 230 Volt-V 230-Two hundred and thirty Volts
V (Italic) = 230 V ± 10% VCA 230 ± 10%-Vac 230 ± 10%-230 VAC ± 10%
V (Italic) = 24 V ± 5% VCC 24 ± 5%-VCC 24 ± 5%-24 VDC ± 5%
50 Hz-Fifty Hertz 50 Hz-Fifty Hz-Hz 50
16 A-Sixteen amperes 16 Ampere-16 AMP-Sixteen amperes
6 KA-Sei kiloampere 6 ka-6 ka-ka 6-Six kiloamperes
3 KW-Three kilowatt 3 KW-Three kwatt-3 kw-KW 3
6 KWh-Six kilowatt-hours 6 kwh-six kilowatt-hours-kwh 6-6 kilowatt-hours
10 kω-Ten Kilohm 10 kω-10 kiloω-3 Kilohm-kω 10
10 mω-Ten Meg 10 Mohm-mω 10-10 meg
10 μf-Ten MfD 10 Microfarads-μf 10-Ten μf
6 S-SEI Siemens S 6-Six Siemens-SEI s-6 s
5 °c-five degrees Celsius 5 °-5 degrees °c-4°c
2 Pa-Due Pascal  PA 2-Two Pascal-two PA
4 N-Four Newton N 4-4 Newton-four n
80 m-Eighty meters 80 MT-M 80-80 linear meters-MT 80
4 m2-Four square meters 4 sqm-M2 4-4 square meters
9 m3-nine cubic meters 9 MC-9 Cubic meters-M3 9
8 LX-Otto Lux 8 Lux-Otto LX-LX 8
5 S-Five seconds 5 sec-S 5-5 S.  -5 Seconds
8 min-Eight minutes 8 min.  -Eight min-min 8
2 H-Two hours 2 H-2 hrs-H 2-hour 2
2 kg-Two kilograms 3 kg-Three Kili-Kg 3-the weight is three kilograms
2014-03-26-26 March 2014 26-03-2014-26-3-14-2014-3-9
€500-$400 €500-$400

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