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Nuclear Size is expressed in Ferrmi whuch is the order of the nuclear size i.e. 10 raise to power minus 15 metres or 10^(-15) metres. Basically, you are asking about measuring the diameter of nucleus of an atom which is a length. Hence, It's SI unit is still metre.
But Fermi is not the SI unit initself, it is the order like Picometer(10^-12 metres), Angstrom(10^-10 meteres) etc. Don't confuse with order and SI unit.
SI units is a system of physical units, set by International System of Units. They are set for
Length(metre), Mass(Kg), Time(second), Temperature(Kelvin), Electric Current(Ampere), Luminosity(candela) and Amount of substance(mole).
*** For ease of expressing them in calculations, expressions, conversations etc we used to write directly order after the numerical result if these results often come in that scale. For example, a person doing nuclear physics will always get numerical values which are of order fermi.
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