A unit of measurement is a definite amount of a
physical quantity, defined and adopted by
convention, that is used as a standard for measurement of the same
physical quantity of any amount. A unit is given a universally
recognised symbol that represents the definite amount of the
physical quantity. For measurement, a pure number is written before
the unit that indicates how many times the predefined amount of the
concerned physical quantitiy is meant.
For e.g., Length is a physical quantity. Metre is a unit of length
that represents a definite predetermined length. The symbol of
metre is 'm'. When we say 10 metres or 10 m, we actually mean 10
times the definite predetermined length called metre.
The definition, agreement, and practical use of
units of
measurement have played a crucial role in human endeavour
from early ages up to this day. Disparate
systems of measurement used to be
very common. Now there is a global standard, the
International System (SI) of units, the modern form of
the
metric system. The SI has been or
is in the
process of being adopted
throughout the world.
In trade,
weights and measures is often a subject
of governmental regulation, to ensure fairness and transparency.
The
Bureau
international des poids et mesures (BIPM) is tasked with
ensuring worldwide uniformity of measurements and their
traceability to the International System of Units (SI).
Metrology is the science for developing national
and internationally accepted units of weights and measures.
In
physics and
metrology, units are standards for
measurement of
physical quantities that need clear
definitions to be useful.
Reproducibility of experimental results is
central to the
scientific method.
A standard system of units facilitates this. Scientific systems of
units are a refinement of the concept of weights and measures
developed long ago for commercial purposes.
Science,
medicine,
and
engineering often use larger and
smaller units of measurement than those used in everyday life and
indicate them more precisely. The judicious selection of the units
of measurement can aid researchers in
problem solving (see, for example,
dimensional analysis).
In the
social sciences, there are no
standard units of measurement and the theory and practice of
measurement is studied in
psychometrics and the
theory of conjoint
measurement.
Systems of measurement
Traditional systems
Prior to the near global adoption of the metric system many
different systems of measurement had been in use. Many of these
were related to some extent or other. Often they were based on the
dimensions of the human body according to the proportions described
by
Marcus Vitruvius Pollio.
As a result, units of measure could vary not only from location to
location, but from person to person.
Metric systems
A number
of metric systems of units have
evolved since the adoption of the original metric system in
France in 1791. The current international standard
metric system is the
International system of
units. An important feature of modern systems is
standardization. Each unit has a universally
recognized size.
Both the
Imperial units and
US customary units derive from earlier
English units. Imperial units were
mostly used in the
British
Commonwealth and the former
British
Empire.
US customary units are still the main system
of measurement used in the United States despite Congress having legally authorized metric
measure on 28 July 1866. Some steps towards US
metrication have been made, particularly the
redefinition of basic US units to derive exactly from SI units, so
that in the US the inch is now defined as 0.0254 m (exactly),
and the avoirdupois pound is now defined as 453.59237 g
(exactly)
Natural systems
While the above systems of units are based on arbitrary unit
values, formalised as standards, some unit values occur naturally
in science. Systems of units based on these are called
natural units. Similar to natural units,
atomic units (au) are a convenient
system of units of measurement used
in
atomic physics.
Also a great number of
unusual and
non-standard units may be encountered. These may include the
Solar mass, the
Megaton (1,000,000 tons of
TNT), and the
Hiroshima atom
bomb.
Legal control of weights and measures
To reduce the incidence of retail fraud, many national
statutes have standard definitions of weights and
measures that may be used (hence "statute measure"), and these are
verified by legal officers.
Base and derived units
Different systems of units are based on different choices of a set
of
fundamental units.The most
widely used system of units is the International System of Units,
or
SI. There are seven
SI
base units. All
other SI units
can be derived from these base units.
For most quantities a unit is absolutely necessary to communicate
values of that physical quantity. For example, conveying to someone
a particular length without using some sort of unit is impossible,
because a length cannot be described without a reference used to
make sense of the value given.
But not all quantities require a unit of their own. Using physical
laws, units of quantities can be expressed as combinations of units
of other quantities. Thus only a small set of units is required.
These units are taken as the
base units. Other units are
derived units. Derived units are a matter of convenience,
as they can be expressed in terms of basic units. Which units are
considered base units is a matter of choice.
The base units of SI are actually not the smallest set possible.
Smaller sets have been defined. For example, there are unit sets in
which the
electric and
magnetic field have the same unit. This is
based on physical laws that show that electric and magnetic field
are actually different manifestations of the same phenomenon.
Calculations with units
Units as dimensions
Any value of a
physical quantity
is expressed as a comparison to a unit of that quantity. For
example, the value of a physical quantity
Z is expressed
as the product of a unit [Z] and a numerical factor:
- Z = n \times [Z] = n [Z].
The multiplication sign is usually left out, just as it is left out
between variables in scientific notation of formulas. The
conventions used to express quantities is referred to as
quantity calculus. In formulas the unit
[Z] can be treated as if it were a specific magnitude of a kind of
physical
dimension: see
dimensional analysis for more on this
treatment.
A distinction should be made between units and standards. A unit is
fixed by its definition, and is independent of physical conditions
such as temperature. By contrast, a standard is a physical
realization of a unit, and realizes that unit only under certain
physical conditions. For example, the metre is a unit, while a
metal bar is a standard. One metre is the same length regardless of
temperature, but a metal bar will be one metre long only at a
certain temperature.
Guidelines
- Treat units algebraically. Only add like terms. When a unit is
divided by itself, the division yields a unitless one. When two
different units are multiplied, the result is a new unit, referred
to by the combination of the units. For instance, in SI, the unit
of speed is metres per second (m/s). See dimensional analysis. A unit can be
multiplied by itself, creating a unit with an exponent (e.g.
m^{2}/s^{2}). Put simply, units obey the laws of
indices.(See Exponentiation)
- Some units have special names, however these should be treated
like their equivalents. For example, one newton (N) is equivalent
to one kg·m/s^{2}. Thus a quantity may have several unit
designations, for example: the unit for surface tension can be referred to as either
N/m (newtons per metre) or kg/s^{2} (kilograms per second
squared). Whether these designations are equivalent is disputed
amongst metrologists.
Expressing a physical value in terms of another unit
Conversion of units involves
comparison of different standard physical values, either of a
single physical quantity or of a physical quantity and a
combination of other physical quantities.
Starting with:
- Z = n_i \times [Z]_i
just replace the original unit [Z]_i with its meaning in terms of
the desired unit [Z]_j, e.g. if [Z]_i = c_{ij} \times [Z]_j,
then:
- Z = n_i \times (c_{ij} \times [Z]_j) = (n_i \times c_{ij})
\times [Z]_j
Now n_i and c_{ij} are both numerical values, so just calculate
their product.
Or, which is just mathematically the same thing, multiply
Z by unity, the product is still
Z:
- Z = n_i \times [Z]_i \times ( c_{ij} \times [Z]_j/[Z]_i )
For example, you have an expression for a physical value
Z
involving the unit
feet per second ([Z]_i) and you want it
in terms of the unit
miles per hour ([Z]_j):
- Find facts relating the original unit to the desired
unit:
- 1 mile = 5280 feet and 1 hour = 3600 seconds
- Next use the above equations to construct a fraction that has a
value of unity and that contains units such that, when it is
multiplied with the original physical value, will cancel the
original units:
- 1 = \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}\quad
\mathrm{and}\quad 1 = \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}
- Last,multiply the original expression of the physical value by
the fraction, called a conversion
factor, to obtain the same physical value expressed in
terms of a different unit.
- Note: since valid conversion factors are dimensionless and have a numerical value of
one, multiplying any physical quantity by such a
conversion factor (which is 1) does not change that physical
quantity.
- 52.8\,\frac{\mathrm{ft}}{\mathrm{s}} =
52.8\,\frac{\mathrm{ft}}{\mathrm{s}}
\frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}
\frac{3600\,\mathrm{s}}{1\,\mathrm{h}} =
\frac {52.8 \times 3600}{5280}\,\mathrm{mi/h}
= 36\,\mathrm{mi/h}
Or as an example using the metric system, you have a value of fuel
economy in the unit
litres per 100 kilometres and you want
it in terms of the unit
microlitres per metre:
- \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}} =
\mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}}
\mathrm{\frac{1000000\,\rm{\mu L}}{1\,\rm{L}}}
\mathrm{\frac{1\,\rm{km}}{1000\,\rm{m}}} =
\frac {9 \times 1000000}{100 \times 1000}\,\mathrm{\mu L/m} =
90\,\mathrm{\mu L/m}
Real-world implications
One
example of the importance of agreed units is the failure of the
NASA Mars Climate
Orbiter, which was accidentally destroyed on a mission to the
planet Mars in September
1999 instead of entering orbit, due to
miscommunications about the value of forces: different computer
programs used different units of measurement (newton versus pound
force). Enormous amounts of effort, time, and money were
wasted.
On
April 15 1999 Korean Air cargo flight 6316 from Shanghai to Seoul was lost due
to the crew confusing tower instructions (in metres) and altimeter
readings (in feet). Three crew and five people on the ground
were killed. Thirty seven were injured.
In 1983, a
Boeing 767 (which came to be know as the Gimli Glider) ran out of fuel in mid-flight because of two
mistakes in figuring the fuel supply of Air
Canada's first aircraft to use metric measurements. This
accident is apparently the result of confusion both due to the
simultaneous use of metric & Imperial measures as well as mass
& volume measures.
See also
Notes
- as amended by Public Law 110–69 dated August 9, 2007
External links
General
Legal
Metric information and associations
Imperial/U.S. measure information and associations