Why can a factor such as 1000m1km be multiplied to any physical quantity without changing its value?
a) Any ratio whose numerator and denominator have the same physical dimension can be inserted into a calculation, irrespective of its numerical value.
b) Since a kilometre is larger than a metre, putting the larger unit in the numerator keeps the overall product unchanged.
c) Its numerical value equals 1 and it is dimensionless.
d) Multiplying by 1000m1km merely changes the units to kilometres; the numerical value will readjust later, so the physical quantity remains the same.