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%TCIDATA{<META NAME="Title" CONTENT="Reference/Physics/International System of Units">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 20:39:08 1997}
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\section{SI Units}

The letters SI stand for Syst\`{e}me International d'Unit\'{e}s. This is the
internationally agreed upon system of coherent units that is now in use for
all scientific and most technological purposes in many countries. SI units
are based on the MKS system and replace the units used in the CGS system and
the f.p.s. system (Imperial units). SI units are of three kinds: the \emph{%
base}, \emph{supplementary}, and \emph{derived units}. There are seven base
units for the seven dimensionally independent physical quantities.

\begin{tabular}{lll}
\multicolumn{3}{c}{\textbf{Base SI Units}} \\ \hline
\textit{Physical quantity} & \textit{Name} & \textit{Symbol} \\ \hline
length & \hyperref{meter}{}{}{Meter.tex} & $\unit{m}$ \\ 
mass & \hyperref{kilogram}{}{}{Kilogram.tex} & $\unit{kg}$ \\ 
time & \hyperref{second}{}{}{Second.tex} & $\unit{s}$ \\ 
electric current & \hyperref{ampere}{}{}{Ampere.tex} & $\unit{A}$ \\ 
thermodynamic temperature & \hyperref{kelvin}{}{}{Kelvin.tex} & $\unit{K}$
\\ 
amount of substance & \hyperref{mole}{}{}{Mole.tex} & $\unit{mol}$ \\ 
luminous intensity & \hyperref{candela}{}{}{Candela.tex} & $\unit{cd}$ \\ 
\hline
\end{tabular}

\begin{tabular}{lll}
\multicolumn{3}{c}{\textbf{Supplementary SI Units}} \\ \hline
\textit{Physical quantity} & \textit{Name} & \textit{Symbol} \\ \hline
plane angle & radian & $\unit{rad}$ \\ 
solid angle & steradian & $\unit{sr}$ \\ \hline
\end{tabular}

\begin{tabular}{lll}
\multicolumn{3}{c}{\textbf{Derived SI Units with Special Names}} \\ \hline
\textit{Physical quantity} & \textit{Name} & \textit{Symbol} \\ \hline
frequency & \hyperref{hertz}{}{}{Hertz.tex} & $\unit{Hz}$ \\ 
energy & \hyperref{joule}{}{}{Joule.tex} & $\unit{J}$ \\ 
force & \hyperref{newton}{}{}{Newton.tex} & $\unit{N}$ \\ 
power & \hyperref{watt}{}{}{Watt.tex} & $\unit{W}$ \\ 
pressure & \hyperref{pascal}{}{}{Pascal.tex} & $\unit{Pa}$ \\ 
electric charge & \hyperref{coulomb}{}{}{Coulomb.tex} & $\unit{C}$ \\ 
electric potential difference & \hyperref{volt}{}{}{Volt.tex} & $\unit{V}$
\\ 
electric resistance & \hyperref{ohm}{}{}{Ohm.tex} & $\unit{\UNICODE{0x3a9}}$
\\ 
electric conductance & \hyperref{siemens}{}{}{Siemens.tex} & $\unit{S}$ \\ 
electric capacitance & \hyperref{farad}{}{}{Farad.tex} & $\unit{F}$ \\ 
magnetic flux & \hyperref{weber}{}{}{Weber.tex} & $\unit{Wb}$ \\ 
inductance & \hyperref{henry}{}{}{Henry.tex} & $\unit{H}$ \\ 
magnetic flux density\hyperref{*}{}{}{magnetic induction} & \hyperref{tesla}{%
}{}{Tesla.tex} & $\unit{T}$ \\ 
luminous flux & \hyperref{lumen}{}{}{Lumen.tex} & $\unit{lm}$ \\ 
illumination & \hyperref{lux}{}{}{lux.tex} & $\unit{lx}$ \\ \hline
\end{tabular}

*\label{magnetic induction}Also known as magnetic induction

SI units are used with a set of fourteen prefixes to form decimal multiples
and submultiples of the units.

\begin{tabular}{lll|lll}
\multicolumn{6}{c}{\textbf{Prefixes Used with SI Units}} \\ \hline
\multicolumn{3}{c|}{\textit{Name of}} & \multicolumn{3}{|l}{\textit{Name of}}
\\ 
\textit{Factor} & \textit{Prefix} & \textit{Symbol} & \textit{Factor} & 
\textit{Prefix} & \textit{Symbol} \\ \hline
$10$ & deca- & da & $10^{-1}$ & deci- & d \\ 
$10^{2}$ & hecto- & h & $10^{-2}$ & centi- & c \\ 
$10^{3}$ & kilo- & k & $10^{-3}$ & milli- & m \\ 
$10^{6}$ & mega- & M & $10^{-6}$ & micro- & $\mu $ \\ 
$10^{9}$ & giga- & G & $10^{-9}$ & nano- & n \\ 
$10^{12}$ & tera- & T & $10^{-12}$ & pico- & p \\ 
$10^{15}$ & peta- & P & $10^{-15}$ & femto- & f \\ 
$10^{18}$ & exa- & E & $10^{-18}$ & atto- & a \\ \hline
\end{tabular}

A number of conventions are observed in the printing or writing of SI units.
Symbols for a prefix are written next to the symbol for the unit without a
space, e.g. $\unit{cm}$, but a space is left between symbols for units in
derived units, e.g. $\unit{N}$ $\unit{m}$ for newton meter. The letter 
\textit{s} is never added to a symbol to indicate a plural; 10 $\unit{ms}$
indicates ten milliseconds, not ten meters. Compound prefixes are never
used, e.g. $\unit{nm}$ for $10^{-9}$ is correct, m$\mu \unit{m}$ is
incorrect. A symbol for a unit with a prefix attached is regarded as a
single symbol which can be raised to a power without using brackets, e.g. $%
\unit{cm}^{2}$ means (0.01 $\unit{m}$)$^{2}$. The word gram has a special
place in SI units; although it is not an SI unit itself, prefixes are
attached to the symbol $\unit{g}$ and not to $\unit{kg}$, e.g. $10^{3}\unit{%
kg}$ is written Mg and not kkg. When writing numbers with SI units the
digits are arranged in groups of three, but a space rather than a comma is
placed between each group. E.g. $10^{5}$ is written 100 000 not 100,000 and $%
10^{-5}$ is written 0.000 01. If a number consists of only 4 digits it is
written without spaces, e.g. 1000 or 0.0001.

SI units make quite clear the relationship between a physical quantity (say
length \textit{l}) and the units in which it is expressed, i.e.

Physical quantity = numerical value $\times $ unit

Or, in the case of length, $l=n\unit{m}$

where $n$ is a numerical. value and $\unit{m}$ is the agreed symbol for the
SI unit of length, the meter. This equation should be treated algebraically,
e.g. the axis of a graph or a column of a table giving numerical values in
meters should be labelled $l/\unit{m}$. If the axis or column gives the
values of $1/l$, it should be labelled $\unit{m}/l$.

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