1


2

 Know the history of the SI System.
 Know the distinction between dimensions and units.
 Know the SI base units, derived units, and the SI prefixes.
 Know how to apply conversion factors from SI to other systems of units.
 What is dimensional homogeneity?

3

 The creation of the decimal Metric System at the time of the French
Revolution and the subsequent deposition of two platinum standards
representing the meter and the kilogram, on 22 June 1799, in the
Archives de la République in Paris can be seen as the first step in the
development of the present International System of Units.

4

 In 1832, Gauss strongly promoted the application of this Metric System,
together with the second defined in astronomy, as a coherent system of
units for the physical sciences. Gauss was the first to make absolute
measurements of the earth's magnetic force in terms of a decimal system
based on the three mechanical units millimeter, gram and second for,
respectively, the quantities length, mass and time. In later years Gauss
and Weber extended these measurements to include electrical phenomena.

5

 These applications in the field of electricity and magnetism were
further developed in the 1860s under the active leadership of Maxwell
and Thomson through the British Association for the Advancement of
Science (BAAS). They formulated the requirement for a coherent system of
units with base units and derived units. In 1874 the BAAS introduced the
CGS system, a threedimensional coherent unit system based on the three
mechanical units centimeter, gram and second, using prefixes ranging
from micro to mega to express decimal submultiples and multiples.

6

 The sizes of the coherent CGS units in the fields of electricity and
magnetism, proved to be inconvenient so, in the 1880s, the BAAS and the
International Electrical Congress, predecessor of the International
Electrotechnical Commission (IEC), approved a mutually coherent set of
practical units. Among them were the ohm for electrical resistance, the
volt for electromotive force, and the ampere for electric current.

7

 After the establishment of the Meter Convention on 20 May 1875 the CIPM
concentrated on the construction of new prototypes taking the meter and
kilogram as the base units of length and mass. In 1889 the 1st CGPM
sanctioned the international prototypes for the meter and the kilogram.
Together with the astronomical second as unit of time, these units
constituted a threedimensional mechanical unit system similar to the
CGS system, but with the base units meter, kilogram and second.

8

 In 1901 Giorgi showed that it is possible to combine the mechanical
units of this meterkilogramsecond system with the practical electric
units to form a single coherent fourdimensional system by adding to the
three base units, a fourth base unit of electrical nature, such as the
ampere or the ohm, and rewriting the equations occurring in electromagnetism
in the socalled rationalized form. Giorgi's proposal opened the path to
a number of new developments.

9

 After the revision of the Meter Convention by the 6th CGPM in 1921,
which extended the scope and responsibilities of the BIPM to other
fields in physics, and the subsequent creation of the CCE (now CCEM) by
the 7th CGPM in 1927, the Giorgi proposal was thoroughly discussed by
the IEC and the IUPAP and other international organizations. This led
the CCE to recommend, in 1939, the adoption of a fourdimensional system
based on the meter, kilogram, second and ampere, a proposal approved by
the ClPM in 1946.

10

 Following an international inquiry by the BIPM, which began in 1948, the
10th CGPM, in 1954, approved the introduction of the ampere, the kelvin and
the candela as base units, respectively, for electric current,
thermodynamic temperature and luminous intensity. The name International
System of Units (SI) was given to the system by the 11th CGPM in 1960.
At the 14th CGPM in 1971 the current version of the SI was completed by
adding the mole as base unit for amount of substance, bringing the total
number of base units to seven.

11

 1793 The meter was first defined by dividing the length from the north
pole to the equator measured along a great circle passing through the
poles into ten million parts.
 The meter was reproduced in metallic bars.
 It was found, however, at a later time that the bar lengths did not
correspond exactly to the original definition.
 So, the original definition was abandoned.

12

 1872 Decision taken to make prototype meters, with the original meter
held in the Archives de France serving as the reference. (The original
meter and kilogram, called the "Mètre des Archives" and
"Kilogramme des Archives", were constructed in 1799 to be one
tenmillionth of a quadrant of the Earth and the mass of a cubic
decimeter of water respectively).
 1875 Convention of the Meter signed.

13

 187889 Selection of Meter and Kilogram prototypes which became the
international prototypes. Distribution of the national prototypes. On 28
September 1889 the International Prototypes were deposited at the BIPM,
where they remain today.

14

 1887 Michelson proposed the use of optical interferometers for the
measurement of length. He subsequently received the 1907 Nobel Prize for
physics for, among other things, his metrological work.
 189293 The Michelson interferometer was used at the BIPM (by Michelson
and Benoît) to determine the length of the meter in terms of the
wavelength of the red line of cadmium.

15

 1906The above measurement was confirmed by Benoît, Fabry and Perot
using the interferometer made by Perot and Fabry.
 192136 First verification of the national prototypes by
intercomparisons among themselves and by comparisons with the
International Prototype. This included new and improved determinations
of the thermal expansion of the meter bars.

16

 1927 International accord, using the above 1893 and 1906 determinations
of the wavelength of the red line of cadmium, defining the ångström; the
ångström thus defined was henceforth used as the spectroscopic unit of
length until abandoned in 1960.
 1952 The CIPM decided to investigate the possibility of redefining the
meter in terms of a wavelength of light.

17

 1960 The CGPM adopted a definition of the meter in terms of the
wavelength in vacuum of the radiation corresponding to a transition
between specified energy levels of the krypton 86 atom.
 1975 The CGPM recommended a
value for the speed of light in vacuum as a result of measurements of
the wavelength and the frequency of laser radiation.

18

 1983 The CGPM redefined the
meter as the length of the path traveled by light in vacuum during a
specific fraction of a second.
 1992 The CIPM decided, on the
basis of new work in national laboratories and at the BIPM, to reduce
significantly the uncertainties associated with the laser radiations
recommended in 1983 and to increase their number from five to eight.

19

 2000 The meter is defined as the length of the path traveled by light
in a vacuum during the time interval of 1/299792458 of a second.

20

 The reason why "kilogram" is the name of a base unit of the SI
is an artifact of history.
 Louis XVI charged a group of savants to develop a new system of
measurement. Their work laid the foundation for the "decimal metric
system", which has evolved into the modern SI. The original idea of
the king's commission (which included such notables as Lavoisier) was to
create a unit of mass that would be known as the "grave".

21

 By definition it would be the mass of a liter of water at the ice point
(i.e. essentially 1 kg). The definition was to be embodied in an
artifact mass standard. After the Revolution, the new Republican
government took over the idea of the metric system but made some
significant changes. For example, since many mass measurements of the
time concerned masses much smaller than the kilogram, they decided that
the unit of mass should be the "gramme".

22

 However, since a onegramme standard would have been difficult to use as
well as to establish, they also decided that the new definition should
be embodied in a onekilogramme artifact. This artifact became known as
the "kilogram of the archives". By 1875 the unit of mass had
been redefined as the "kilogram", embodied by a new artifact
whose mass was essentially the same as the kilogram of the archives.

23

 The decision of the Republican government may have been politically
motivated; after all, these were the same people who condemned Lavoisier
to the guillotine. In any case, we are now stuck with the infelicity of
a base unit whose name has a "prefix".

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26


27

 Unit of time (second) The second is the duration of 9,192,631,770
periods of the radiation corresponding to the transmission between two
hyperfine levels of the ground state of the cesium133 atom.

28

 Unit of electric current (ampere) The ampere is that constant current
which, if maintained in two straight parallel conductors of infinite
length of negligible circular cross section, and placed one meter apart
in a vacuum, would produce between these conductors a force equal to 2 x
10^{7} newton per meter of length.

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30

 Unit of amount of substance (mole) The mole is the amount of substance
that contains as many elementary entities as there are atoms in 0.012 kg
of carbon12. When the mole is
used, the elementary entities must be specified and may be atoms,
molecules, electrons, other particles, or specified groups of particles
(Avogadro’s no. =6.022 x 10^{23)}.

31

 Unit of luminous intensity (candela) The candela is the luminous
intensity, in a given direction, of a source that emits monochromatic
radiation of a frequency 540 x 10^{12} cycles per second and
that has a radiant intensity in that direction of (1/683) watt per
steradian.

32

 Prefix dec. eq. exp eq.
 Pico 0.000000000001 10^{12}
 Nano 0.000000001 10^{9}
 Micro 0.000001 10^{6}
 Milli 0.001 10^{3}
 Centi 0.01 10^{2}
 Deci 0.1 10^{1}
 no prefix 1.0 10^{0}

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 Prefix dec. eq. exp eq.
 Deka 10.0 10^{1}
 Hecto 100.0 10^{2}
 Kilo 1000.0 10^{3}
 Mega 1,000,000. 10^{6}
 Giga 1,000,000,000. 10^{9}

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 1. Regular upright type is used and the symbol is written in lower case
except if derived from a proper name (i.e., N for newton. L for liter is
used to avoid confusion with the number 1.
 2. The unit names are always written in lower case letters, even if
derived from a proper name (i.e., newton).

37

 3. Units symbols are unaltered in the plural.
 4. Plurals of the unit names are made using the rules of English
grammar.
 5. Do not use selfstyled abbreviations (i.e., sec for second).
 6. A space is placed between the symbol and a number.
 7. There is no period following the symbol except if it occurs at the
end of a sentence.

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 8. When a quantity is expressed as a number and unit, and is used as an
adjective, then a hyphen separates the number and unit. For example: The
3m rod broke.
 9. The product of two or more unit symbols may be indicated with a
raised dot or a space. (N^{.}m or N m).
 10. The product of two or more unit names is indicated by a space
(preferred) or a hyphen.

39

 11. A solidus (oblique stroke,/), a horizontal line, or negative
exponents may be use to express a derived unit formed from others by
division.
 12. The solidus must not be repeated on the same line unless ambiguity
can be avoided by parentheses.
 13. When using the solidus notation, multiple symbols in the denominator
must be enclosed in parentheses. Example: m^{.}kg/(s^{3.}A).

40

 14. The SI units names that contain a ratio or quotient, use the word
per rather than the solidus.
 15. Power of units use the modifier squared or cubed after the unit
name.
 16. Symbols and unit names should not be mixed in the same expression.
NOT: J/kilogram.
 17. SI prefix symbols are written is regular upright type (no hyphen
between the prefix and the unit symbol).

41

 18. The entire name of the prefix is attached to the unit name. No space
or hyphen separates them (five milliseconds).
 19. The grouping formed by the prefix symbol attached to the unit symbol
constitutes a new inseparable symbol that can be raised to a positive or
negative power and that can be combined with other unit symbols to form
compound unit symbols (1cm^{3}= (10^{2} m)^{3}
= 10^{6} m^{3}).

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 20. Compound prefixes formed by combining two or more SI prefixes are
not permitted ( 1 mg but NOT 1 mkg).
 21. A prefix must have an attached unit and should never be used alone.
 22. Modifiers are not to attached to the units (V of alternating
current).
 23. Use one prefix in compound units (mV/m NOT mV/mm).

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 24. Dimensionless numbers are not required to have the units reported.
For example refractive indices do not have units and may be reported as
1.33.
 25. Units such as “parts per thousand”
may be used. It is necessary, however, to explain what the “part”
is .
 26. Unit symbols are preferred to unit names (15 m rather than 15
meters).

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