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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 $299792458m/s$, 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.^[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.

A unit of time is a reference duration used to express a time interval. Writing $\Delta t=2\min =120\mathrm{s}$ changes the numerical representation, not the elapsed time in physics. A date labels a point on a time scale; a duration measures separation between two such points.

The SI base unit is the second, defined by fixing the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom to exactly $9192631770\mathrm{Hz}$. A clock realizes that definition by comparing an oscillator with the atomic response; practical imperfections still create measurement uncertainty.^[ref]

A minute is exactly 60 seconds, an hour 3600, and a day used as a duration unit 86400. A calendar day need not coincide with a uniform 86400-second interval on every civil time scale. Specifying the time convention matters when combining clock measurements, astronomical observations and Julian years.