Measurement

Physical measurement is the estimation or determination of a specific dimension (length, capacity, etc.), usually in relationship with a standard or unit of measurement

The result of the physical measurement is expressed in terms of the multiple of the standard. Example: measuring distances (kilometers, miles, leagues) or measuring time (seconds, hours)

A magnitude is measurable when we can define equality and ratio (or sum) of two magnitudes of his type

The number that measures a magnitude is the ratio of that magnitude to the size of the same species chosen for unity

So the physical measurement process involves estimating the ratio from the magnitude of a quantity to that of a unit of the same type. A physical measurement is the result of such a process, expressed as the product of a real number and a unit, in which the real is the estimated report. Unlike an account, that is, a quantity of objects known exactly, each physical measure is actually an estimate and therefore has some uncertainty.

Physical measurement is the estimation or determination of a specific dimension (length, capacity, etc.), usually in relationship with a standard or unit of measurement. The result of the physical measurement is expressed in terms of the multiple of the standard. Example: measuring
distances (kilometers, miles, leagues) or measuring time (seconds, hours).

A magnitude is measurable when we can define equality and ratio (or sum) of two magnitudes of his type.

The number that measures a magnitude is the ratio of that magnitude to the size of the same species chosen for unity.

Overview

Before the units of the international system are adopted all over the world (Only Myanmar, Liberia, and the United States do not use SI as their official system of measurement.

In these countries, though, SI is commonly used in science and medicine.), there were many systems, more or less practical and more or less generalized in terms of areas of expansions, professional or other uses. The International System of Units (abbreviated as SI) is the form modern and
revised metric system.

It is the General Conference of Weights and Measures, bringing together delegates from Member States of the Meter Convention, which decides the evolution of the system, every four years, in Paris. The abbreviation of
“Système International” is SI, regardless of the language used.

The International Standard ISO 1000 (ICS 01 060) describes the units of the International System and the recommendations for the use of their multiples and some other units.

The SI was developed in the 1960s from the system MKS (meter-kilogram-second) preferentially to the system CGS (centimeter-gram-second), which has multiple variants

There are two types of SI units, base units and units secondary. The basic units are the measures corresponding to the time, length, mass, temperature, quantity (of objects), electric current, and light intensity. The units secondary are built on basic units; like example the density expressed in kg∕m³.

Example: length is a measurable quantity; having two wires, we know how to define their equality, if, stretched rectilinearly, they have the same ends. We know how to define their sum by putting them end-to-end choosing a standard unit, the meter (symbol m), any length will put in the form L = lm

If g is the number that measures the magnitude G with the unit U, G = gU G. G has the dimension of U

In a historic vote, the BIPM Member States adopted, on 16 November 2018, the revision of the International System of Units (SI), thus modifying the world definition of the kilogram, the ampere, the kelvin and the mole

The revision of the IS, adopted by the General Conference of Weights and Measures (GFCM) at its 26th meeting in Versailles, has the consequence that all SI units will now be defined from constants of nature, which will ensure the stability of the IS in the future and will pave the way for the use of new technologies, including quantum technologies, to put into practice the definitions.

Universal physical constants

Do not confuse the notion of mathematical constants whose value without a fixed dimension. Example:

And that of dimensioned physical constants, whose value is fixed in a certain choice of units. Example: speed of light in the vacuum

Orthographic and typographical Rules

Name of the units

The name of the units is a common name even though the unit is drifting a proper name. The first letter of the name of a unit is so always a tiny one. One writes thus ampere, second and degree Celsius (this is not the first letter that is capitalized)

To form the names of the multiple and sub-multiple units, prefixes are simply contiguous

In case of product of units, we use a dash or an unsecable-space (non-breaking space) in the name of the unit derivative. Thus, the correct spellings of the unit whose symbol is kWh are kilowatt-hour and kilowatt
hour

It is forbiden to stick together several prefixes to a unit (nanometer but not millimicrometer)

Symbol of the units

Unit symbols start with an uppercase (capital letter)if the unit does derive from a proper name and a lowercase if not. for example, the symbols of the pascal (Pa) and the second (s)

The symbol of the liter is a notable exception to this rule. l or L are accepted to avoid confusion with the number 1

Unit symbols are always written in Roman characters whatever the font of the text where they appear

Unit symbols constitute mathematical entities and not abbreviations; so we write 30 cm and not 30 cms. Abbreviations of symbols and unit names (such as sec for the second (s) or cc for cubic centimeter (cm3)) are prohibited

do not mix symbols (mathematical entities) and names units ; so we will always write newton per kilogram and never newton per kg

Finally the ratings of the division and the multiplication apply to the symbols of the derived units: thus one can write the symbol of the meter per second m.s^-1, m∕s or and the kilowatt hour kW h or kW · h. To avoid ambiguous notations, we never use more than one slash in the symbol of a unit: A / m / s could be the symbol of the ampere per meter per second (A ⋅ m^-1 ⋅ s^-1 or A∕(m ⋅ s)) or that of the second ampere per meter (A ⋅ m^-1 ⋅ s or
A ⋅ s∕m)

The symbols of the units must be preceded by a non-breaking space (except for unit symbols sexagesimales angle: 40^∘16′25”), so we write 30 cm and not 30cm.

Units

A new system

At its 25th meeting the GFCM changed completely the system of units. considering that :

it is essential to have a uniform and globally accessible International System of Units (SI) for international trade, high technology industry,
human health and safety, protection of the environment, climate change studies, and the basic science that underpins all these areas
the SI units must be stable in the long term, self-consistent and practically feasible, based on the current theoretical description of nature, at the highest level
a revision of the SI to meet these requirements was proposed in Resolution 1, adopted unanimously by the GFCM at its 24th meeting (2011), which details a new way of defining the IS from a a set of seven constants, chosen from the fundamental constants of physics and other constants of nature, from which the definitions of the seven basic units are deduced,

decides that as of May 20, 2019, the International System of Units, SI, is the system of units in which:

the frequency of the hyperfine transition of the ground state of the undisturbed cesium 133 atom, capital Δ_νCs, is equal to 9192631770 Hz

the speed of light in a vacuum, c, is equal to 299792458m∕s

the Planck constant, h, is equal to 6,62607015 ⋅ 10^-34J.s

the elementary charge, e, is 1,602176634 ⋅ 10^-19C

the Boltzmann constant, k, is equal to 1,380649 ⋅10^-23J∕K

the Avogadro constant, NA, is 6.02214076⋅10²³mol the luminous efficiency of a monochromatic radiation of frequency 540 ⋅ 10¹²Hz, K_cd is equal to 683lm∕W

where the units hertz, joule, coulomb, lumen and watt, which respectively have symbol Hz, J, C, lm and W, are connected to the units second, meter, kilogram, ampere, kelvin, mole and candela, which respectively have symbol s, m, kg, A, K, mol and cd, according to the relations Hz = s^-1,J = kg ⋅ m² ⋅ s^-2, C = A ⋅ s, lm = cd ⋅ m² ⋅ m^-2 = cd ⋅ sr, and W = kg ⋅ m² ⋅ s^-3

The new SI definition based on the fixed numerical values of the chosen constants, makes it possible to deduce the definition of each of the seven basic units of the SI using one or more of these constants, as the case may be . The resulting definitions, which will take effect on May 20, 2019,
are as follows:

The second, symbol s, is the time unit of the SI. It is defined by taking the fixed numerical value of the frequency of cesium, Δν_Cs, the frequency of the hyperfine transition of the ground state of the unaffected cesium 133 atom, equal to 9192631770 when it is expressed. in Hz, unit equal to s^-1.

The meter, symbol m, is the unit length of the SI. It is defined by taking the fixed numerical value of the speed of light in vacuum, c, equal to 299792458 when expressed in m∕s, the second being defined according to Δν_Cs,.

The kilogram, symbol kg, is the mass unit of the SI. It is defined by taking the fixed numerical value of the Planck constant, h, equal to 6,62607015 ⋅ 10^-34 when expressed in J ⋅ s, unit equal to kg⋅m²⋅s^-1, the meter and the second being defined according to c and Δν_Cs,.

The ampere, symbol A, is the unit of electric current of the SI. It is defined by taking the fixed numerical value of the elementary charge, e, equal to 1,602176634 ⋅ 10^-19 when it is expressed in C, unit equal to A ⋅ s, the second being defined according to Δν_Cs,.

The kelvin, symbol K, is the thermodynamic temperature unit of the SI. It is defined by taking the fixed numerical value of the Boltzmann constant,k, equal to 1,380649 ⋅ 10^-23 when it is expressed in J⋅K^-1, unit equal tokg⋅m²⋅s^-2⋅K^-1, the kilogram, the meter and the second being defined according to h, c and Δν_Cs

The mole, mol symbol, is the unit of matter quantity of the SI. One mole contains exactly 6,02214076 ⋅ 10²³ elementary entities. This
number, called « Avogadro number », corresponds to the fixed numerical value of the Avogadro constant, Na, when expressed in mol^-1. The quantity of matter, symbol n, of a system is a representation of the number of elementary entities specified. An elementary entity may be an atom, a molecule, an ion, an electron, or any other particle or specified group of particles.

The candela, symbol cd, is the SI unit of light intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficiency of a monochromatic radiation of frequency 540⋅10¹²Hz, K_cd, equal to 683 when it is expressed in lm⋅W^-1, unit equal to cd⋅sr⋅W⋅ , or cd⋅sr⋅kg^-1 ⋅m^-2 ⋅s³, the kilogram, the meter and the second being defined according to h,c and Δν_Cs .

units

Quantity measured	Unit name	Unit symbol	original definition
length	meter	m	Original (1793): 1/10000000 of the meridian through Paris between the North Pole and the Equator
mass	kilogram	kg	Original (1793): The grave was defined as being the weight [mass] of one cubic decimeter of pure water at its freezing point.
time	seconds	s	Original (Medieval): 1/86400 of a day
electric current	ampere	A	Original (1881): A tenth of the abampere, the unit of current used in the electromagnetic CGS
temperature	kelvin	K	Original (1743): The centigrade scale is obtained by assigning 0° to the freezing point of water and 100° to the boiling point of water
amount of substance	mole	mol	Original (1900): The molecular weight of a substance in mass grams.
luminous intensity	candela	cd	Original (1946): 1/60 of the brightness per square centimeter of a black body at the temperature where platinum freezes.

two more dimension don’t have a unit

radian (rad) plane angle

Steradian (sr) solid angle

prefixes

Very large or very small measurements can be written using prefixes. Prefixes are added to the beginning of the unit to make a new unit. For example, the prefix kilo- means « 1000 » times the original unit and the prefix milli- means « 0.001 » times the original unit. So one kilometre is 1000 metres and one milligram is a 1000th of a gram.

Multiples

Name	Prefix	Factor
		10⁰
deca	da	10¹
hecto	h	10²
kilo	k	10³
mega	M	10⁶
giga	G	10⁹
tera	T	10¹²
peta	P	10¹⁵
exa	E	10¹⁸
zetta	Z	10²¹
yotta	Y	10²⁴

Fraction

Name	Prefix	Factor
		10⁰
deci	d	10^-1
centi	c	10^-2
milli	m	10^-3
micro	μ	10^-6
nano	n	10^-9
pico	p	10^-12
femto	f	10^-15
atto	a	10^-18
zepto	z	10^-21
yocto	y	10^-24

Convertion

The easiest way to perform unit-to-unit conversions is to
use a table. Each column corresponds to a multiple. They
are further subdivided into as many sub-columns as the
dimension of the converted unit.

kg	hg	dag	g	dg	cg	mg
					5	2
			0.	0	5	2

52mg = 0.052g

km²	hm²	dam²		m²		dm²	cm²	mm²
	0,	6
		6	0	0	0

0.6hm² = 6000m²

it is important to note that at NCTP 1L = 1dm³

km³	hm³	dam³	m³		dm³			cm³	mm³
							1
				0,	0	0	1

1L = 0.001m³ or 1m³ = 1000L

Derived units

All the derived units, that is to say the one used every day, derive from these basic units. They are created by combining the base units. The base units can be divided, multiplied, or raised to powers. Some derived units have special names. Usually these were created to make calculations simpler.

example:

Length L. meter m
Surface S = L² square meters m²
Volume V = L³ cubic meter m³
Speed v = L∕T meter per second m ⋅ s^-1
Acceleration a = v∕T meter per second per second m.s^-2
Force F = M.a acceleration time mass kg ⋅ m ⋅ s^-2
Work, Heat Q Or W = F ⋅ L force time length kg ⋅ m² ⋅ s^-2

Measurement uncertainty

In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value.

Approximation on the measure

When measuring a physical quantity G, the numerical value g obtained is directly related to the accuracy of the measurement. For example, a mass will be determined with all the more precision that the scale used will be
accurate.

A physical equality does not therefore translate a « perfect » knowledge of the measured value, but a knowledge « with errors of experience ». For example, measuring a length using a decimeter will only know its value to the nearest millimeter. Most decimeters are graduated in millimeters.

The different types of errors of measured

There are two types of measurement error categories:

- Systematic errors

Accidental errors

Systematic errors

These errors always occur in the same direction. They have
various origins:

- The experimenter

- The measurement method

The measuring device

The experimenter
For example, measuring time using a manual stopwatch
introduces a systematic error due to the lack of reflex the
experimenter.

The measurement method
To perform a precision weighing without considering the
Archimedean thrust is a poorly adapted method leading to
a systematic error. More simply, perform a weighing
without tare previously the container containing the
element will induce systematically an error equal to the
mass of this container.

The measuring device
A measuring device must have three qualities:

Fidelity
A series of measurements made over time must lead to
the same result. Sensitivity: the device established a
correspondence between the reading and the value of the
measured quantity

Sensitivity
is defined by the variation of the reading on the
variation of the magnitude and it must to be very
big

Justness
The relationship between value read and size measured
must be completely accurate. For example a beam balance
is not fair if it is used in simple weighing because the
balance simply indicates the equality of the moments ml =
m’l ’ and not that of the masses. Indeed, the arms can not
be strictly equal.

Whenever we find a systematic error, we try to delete it.
For example, in the case of the chronometer being
human can be replaced by a laser beam that will be
cut by the moving mobile. Or in a double weighing
method the constant tare will eliminate the method
defects of weighing and the lack of accuracy of the
balance even if the arms are unequal. Unfortunately,
some systematic errors remain very difficult to detect
…

Accidental errors

These are errors that vary in size and meaning. They
have the same origins as the previous mistakes. For
the illustrate, let’s use the example of measuring a
length.

An experimenter who measures a length using a
graduated ruler, if it has a good view, estimates the length
0.5 mm near. If he uses a caliper, the measurement will be
made to 0.1 mm near. The reading error is therefore
simultaneously linked to the experimenter and the
measuring instrument. Nevertheless, the experience allows
to evaluate the domain of the error. This domain is called
area of uncertainty. It is associated with a limit absolute
uncertainty or absolute error.

In fact, in many cases of physical measurements, this
absolute error can not be determined in this way. It is
therefore compensated by a statistical evaluation of the
error.

Uncertainty of measures

Uncertainties about a direct measurement

Absolute uncertainty
The maximum difference between the central value
and all others measured values and called absolute
uncertainty.

G = g ± .Δd

g – Δg ≤ G ≤ g + .Δg

Relative uncertainties
Relative uncertainty is the quotient of absolute certainty
on the measured value. This relative uncertainty is still
called accuracy of the measurement.

P = Δg∕g

Absolute uncertainty does not allow comparison directly
results in the accuracy of two measurements of the
same species. By example an absolute uncertainty of 1
mm on a tissue ribbon of 20 cm may seem smaller
than an absolute uncertainty of 10 cm on a track of
athletics of 100 m. The calculation shows that it is not
so.

P = 0.1∕20 = 0.005 that is to say 0.5%

P = 0.1∕100 = 0.001 that is to say 0.1%

Uncertainty over calculated values

Most often the value G that can be determined is not
directly measurable. It is a function of several variables
which are measurable and are connected by a series of
relations leading to G. The problem consists in determining
the error on G knowing the values of the variables,
the errors on these variables and the relation linking
them.

When the relation is of additive type, the absolute
errors will be added.

When the relation is of multiplicative type, the relative
errors will be added.

For more complex relationships, the calculation of the
error will be done step by step.

Example:

G = x + y then dg = dx + dy

G = x – y then dg = dx + dy

G = xy then dg∕g = dx∕x + dy∕y

G = x∕y then dg∕g = dx∕x + dy∕y