= Unit of length
{title2=$\mathrm m$}
A <unit of length> is a specified reference magnitude used to express a <length>. In $\ell=3\,\mathrm m=300\,\mathrm{cm}$, the physical length is unchanged; only its numerical value and chosen unit change. This separates a <physical dimension> from a unit convention.
The SI base unit is the <metre>, symbol $\mathrm m$. It is defined by fixing the vacuum <speed of light> at exactly $299792458\,\mathrm{m/s}$, with the <second> defined independently through the caesium frequency. Thus realizing a metre can connect length measurement to a measured time interval or a calibrated optical frequency.<The International System of Units (SI), ninth edition, SI Brochure>[Section 2.3.1, definition of the metre]{ref}
Unit conversion should preserve dimensions: converting $2\,\mathrm{km}$ to $2000\,\mathrm m$ changes a length by a factor of $1000$ in its numerical representation, while the corresponding area changes by $1000^2$. <Astronomical units>, <light-years> and <parsecs> are useful for different astronomical distance scales; the choice does not alter the distance being measured.
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