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The Système International (SI) is a coherent set
of measurement units |
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The BIPM’s task is to establish standards and
scales for the SI |
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The CIPM supervises the work of the BIPM in
order to ensure world-wide uniformity of measurements |
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The CIPM’s nine Consultative Committees
co-ordinate work in their respective fields |
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The CIPM reports to the CGPM, which initiates
the actions necessary to maintain and improve the SI |
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There are seven base units |
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… and many derived units, which are expressed by
multiplication and division of base units |
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… as well as some non-SI units accepted for use
with the SI |
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Length metre m |
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Mass kilogram kg |
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Time second s |
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Electric current ampere A |
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Thermodynamic temperature kelvin K |
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Amount of
substance mole mol |
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Luminous intensity candela cd |
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The metre is the length of the path
travelled by light in vacuum during a time interval of 1/299 792 458 of a
second |
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The kilogram is the unit of mass; it is
equal to the mass of the international prototype of the kilogram |
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The second is the duration of 9 192 631 770
periods of the radiation corresponding to the transition between the two
hyperfine levels of the ground state of the caesium 133 atom |
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The ampere is that constant current which,
if maintained in two straight parallel conductors of infinite length, of
negligible circular cross-section, and placed 1 metre apart in vacuum,
would produce between these conductors a force equal to 2 x 10-7 newton
per metre of length |
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The kelvin, unit of thermodynamic
temperature, is the fraction 1/273.16 of the thermodynamic temperature of
the triple point of water |
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The mole is the amount of substance of a system
which contains as many elementary entities as there are atoms in 0.012
kilogram of carbon 12; its symbol is “mol”. |
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When the mole is used, the elementary entities
must be specified and may be atoms, molecules, ions, electrons, other
particles, or specified groups of such particles. |
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The candela is the luminous intensity, in a
given direction, of a source that emits monochromatic radiation of
frequency 540 x 1012 hertz and that has a radiant intensity in
that direction of 1/683 watt per steradian. |
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These units are products of powers of base
units. |
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For example: |
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force newton N kg . m .
s-2 |
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energy joule J N . m kg
. m2 . s-2 |
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power watt W J/s kg
. m2 . s-3 |
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emf volt V W/A kg .
m2 . s-3 . A-1 |
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resistance ohm Ω V/A kg
. m2 . s-3 . A-2 |
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absorbed dose
gray Gy J/kg m2 . s-2 |
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Examples: |
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day, hour, minute |
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degree, minute, second |
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litre |
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electronvolt |
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nautical mile and knot |
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hectare |
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bar |
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ångström |
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Factor Name Symbol Factor Name Symbol |
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1024 yotta Y 10-1 deci d |
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1021 zetta Z 10-2 centi c |
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1018 exa E 10-3 milli m |
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1015 peta P 10-6 micro μ |
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1012 tera T 10-9 nano n |
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109 giga G 10-12 pico p |
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106 mega M 10-15 femto f |
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103 kilo k 10-18 atto a |
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102 hecto h 10-21 zepto z |
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101 deca da 10-24 yocto y |
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Components don’t fit together if different
manufacturers use different units |
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International trade depends on a common,
world-wide system of units |
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Scientific research assumes a coherent set of
units which express the fundamental constants of nature |
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Misunderstandings about units can cause
disaster! |
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“Mission specifications called for using
metric units, but the Lockheed group sent navigation information in English
units. The mix-up meant that Lockheed engineers modelled navigation with
pounds force (the English unit for measuring thruster impulse) while JPL
did its calculations in newtons (the metric measurement). One pound force
is equivalent to 4.45 newtons.”
(Report on the loss of NASA’s Mars Orbiter spacecraft) |
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The symbol for the decimal marker must be either
a point on the line or a comma on the line (22nd CGPM 2003) |
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Digits may be divided into groups of three to
facilitate reading: neither dots nor commas are ever inserted in the spaces
between groups (9th CGPM 1948) |
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The number of digits presented should reflect
the accuracy of the result: avoid spurious resolution |
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The number of digits following the decimal
marker should normally be less than three – make use of the SI prefixes |
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Accuracy of measurement is the closeness of
the agreement between the measurement result and the true value of the
measured quantity …….. |
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……. but we don’t generally know the true
value, so …. |
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… the uncertainty of measurement is a
parameter that characterises the dispersion of the values that could
reasonably be attributed to the measured quantity. It is normally expressed in terms of a
standard deviation or as the half-width of an interval having a stated
level of confidence. |
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Uncertainty of measurement may comprise many
components. |
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Some components may be evaluated from the
statistical distribution of the results of series of measurements (Type A) |
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Other components are evaluated from assumed
probability distributions based on experience or other information (Type B) |
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All components can be characterised by
standard deviations and they all contribute to the combined standard
uncertainty of the result of a measurement. |
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Describe the definition of the measurand: what
did you measure? |
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Give the estimate of the measurand: what is the
result of the measurement? |
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Make sure you state the appropriate units of
measurement – SI of course! |
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State the combined standard uncertainty. |
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For a full report, describe how the result and
uncertainty were obtained. Include values of inputs and their
uncertainties, covariances of correlated input estimates, degrees of
freedom of input estimates, and (where possible) functional relationships
between the result and the various inputs. |
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“When you can measure what you are speaking
about and express it in numbers you know something about it; but when you
cannot measure it, when you cannot express it in numbers, your knowledge of
it is of a meagre and unsatisfactory kind” |
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(Lord Kelvin) |
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Notes