The results of measurements are quantities

A quantity is expressed as ………

…. a number ……

The International System of Units (SI)

The Système International (SI) is a coherent set of measurement units

The BIPM’s task is to establish standards and scales for the SI

The CIPM supervises the work of the BIPM in order to ensure world-wide uniformity of measurements

The CIPM’s nine Consultative Committees co-ordinate work in their respective fields

The CIPM reports to the CGPM, which initiates the actions necessary to maintain and improve the SI

The SI units

There are seven base units

… and many derived units, which are expressed by multiplication and division of base units

… as well as some non-SI units accepted for use with the SI

The SI base units

Length metre m

Mass kilogram kg

Time second s

Electric current ampere A

Thermodynamic temperature kelvin K

Amount of substance mole mol

Luminous intensity candela cd

The unit of length (metre)

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

The unit of mass (kilogram)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram

The unit of time (second)

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

The 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 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10^-7newton per metre of length

The unit of thermodynamic temperature (kelvin)

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

The unit of amount of substance (mole)

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”.

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.

The unit of luminous intensity (candela)

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.

The SI derived units

These units are products of powers of base units.

For example:

force newton N kg . m . s^-2

energy joule J N . m kg . m² . s^-2

power watt W J/s kg . m² . s^-3

emf volt V W/A kg . m² . s^-3 . A^-1

resistance ohm Ω V/A kg . m² . s^-3 . A^-2

absorbed dose gray Gy J/kg m² . s^-2

Non-SI units accepted for use with SI

Examples:

day, hour, minute

degree, minute, second

litre

electronvolt

nautical mile and knot

hectare

bar

ångström

Multiples and sub-multiples: the SI prefixes

Factor Name Symbol Factor Name Symbol

10²⁴ yotta Y 10^-1 deci d

10²¹ zetta Z 10^-2 centi c

10¹⁸ exa E 10^-3 milli m

10¹⁵ peta P 10^-6 micro μ

10¹² tera T 10^-9 nano n

10⁹ giga G 10^-12 pico p

10⁶ mega M 10^-15 femto f

10³ kilo k 10^-18 atto a

10² hecto h 10^-21 zepto z

10¹ deca da 10^-24 yocto y

Does it matter if you don’t use SI units?

Components don’t fit together if different manufacturers use different units

International trade depends on a common, world-wide system of units

Scientific research assumes a coherent set of units which express the fundamental constants of nature

Misunderstandings about units can cause disaster!

“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)

And now what about the numbers?

The correct expression of numbers

The symbol for the decimal marker must be either a point on the line or a comma on the line (22^nd CGPM 2003)

Digits may be divided into groups of three to facilitate reading: neither dots nor commas are ever inserted in the spaces between groups (9^th CGPM 1948)

The number of digits presented should reflect the accuracy of the result: avoid spurious resolution

The number of digits following the decimal marker should normally be less than three – make use of the SI prefixes

The expression of measurement uncertainty

Accuracy of measurement is the closeness of the agreement between the measurement result and the true value of the measured quantity ……..

……. but we don’t generally know the true value, so ….

… 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.

The expression of measurement uncertainty

Uncertainty of measurement may comprise many components.

Some components may be evaluated from the statistical distribution of the results of series of measurements (Type A)

Other components are evaluated from assumed probability distributions based on experience or other information (Type B)

All components can be characterised by standard deviations and they all contribute to the combined standard uncertainty of the result of a measurement.

Reporting the measurement result and its associated uncertainty

Describe the definition of the measurand: what did you measure?

Give the estimate of the measurand: what is the result of the measurement?

Make sure you state the appropriate units of measurement – SI of course!

State the combined standard uncertainty.

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.

The complete expression of the result!

Why do we need such small uncertainties?

…. and the title?

“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”

(Lord Kelvin)

Slide 30


	The Système International (SI) is a coherent set of measurement units
	The BIPM’s task is to establish standards and scales for the SI
	The CIPM supervises the work of the BIPM in order to ensure world-wide uniformity of measurements
	The CIPM’s nine Consultative Committees co-ordinate work in their respective fields
	The CIPM reports to the CGPM, which initiates the actions necessary to maintain and improve the SI


	There are seven base units
	… and many derived units, which are expressed by multiplication and division of base units
	… as well as some non-SI units accepted for use with the SI


	Length metre m
	Mass kilogram kg
	Time second s
	Electric current ampere A
	Thermodynamic temperature kelvin K
	Amount of substance mole mol
	Luminous intensity candela cd


	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


	The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram


	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


	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^-7newton per metre of length


	The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water


	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”.
	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.


	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.


	These units are products of powers of base units.

	For example:
		force newton N kg . m . s^-2
		energy joule J N . m kg . m² . s^-2
		power watt W J/s kg . m² . s^-3
		emf volt V W/A kg . m² . s^-3 . A^-1
		resistance ohm Ω V/A kg . m² . s^-3 . A^-2
		absorbed dose gray Gy J/kg m² . s^-2


	Examples:
		day, hour, minute
		degree, minute, second
		litre
		electronvolt
		nautical mile and knot
		hectare
		bar
		ångström


	Factor Name Symbol Factor Name Symbol
	10²⁴ yotta Y 10^-1 deci d
	10²¹ zetta Z 10^-2 centi c
	10¹⁸ exa E 10^-3 milli m
	10¹⁵ peta P 10^-6 micro μ
	10¹² tera T 10^-9 nano n
	10⁹ giga G 10^-12 pico p
	10⁶ mega M 10^-15 femto f
	10³ kilo k 10^-18 atto a
	10² hecto h 10^-21 zepto z
	10¹ deca da 10^-24 yocto y


	Components don’t fit together if different manufacturers use different units
	International trade depends on a common, world-wide system of units
	Scientific research assumes a coherent set of units which express the fundamental constants of nature
	Misunderstandings about units can cause disaster!
		“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)


	The symbol for the decimal marker must be either a point on the line or a comma on the line (22^nd CGPM 2003)
	Digits may be divided into groups of three to facilitate reading: neither dots nor commas are ever inserted in the spaces between groups (9^th CGPM 1948)
	The number of digits presented should reflect the accuracy of the result: avoid spurious resolution
	The number of digits following the decimal marker should normally be less than three – make use of the SI prefixes


	Accuracy of measurement is the closeness of the agreement between the measurement result and the true value of the measured quantity ……..
	……. but we don’t generally know the true value, so ….
	… 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.


	Uncertainty of measurement may comprise many components.
	Some components may be evaluated from the statistical distribution of the results of series of measurements (Type A)
	Other components are evaluated from assumed probability distributions based on experience or other information (Type B)
	All components can be characterised by standard deviations and they all contribute to the combined standard uncertainty of the result of a measurement.


	Describe the definition of the measurand: what did you measure?
	Give the estimate of the measurand: what is the result of the measurement?
	Make sure you state the appropriate units of measurement – SI of course!
	State the combined standard uncertainty.
	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.


	“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”

	(Lord Kelvin)