what makes a quantity a fundamental or base quantity?

Question

what makes a quantity a fundamental or base quantity?

Answer 1

Fundamental quantities are those used to derive other quantities.

Examples are the Meter, Gram, and Liter and second. These derive most other quantities of measure. Learning those derivations will save you life in physics.

Example of a derived quantity is the Newton which is the quantity of force. A newton is a kg m/second squared. How do we get this? The equation for force is F=ma which is Force is the mass times the acceleration. Accelaration is also a derived quantity. It is the velocity change over time. Velocity is also a derived quantity. It is the change in distance over time. Therefore

F=m s/t/t mass is a base (kilograms) distance is a base (meters) and time is a base (seconds).

Have fun.

Answer 2

The base quantities are agreed by the scientific community to be the following seven:

length, mass, time, current, temperature, amount of substance, luminous intensity

each unit of these quantity are clearly defined, for example, the base unit of time is the second and "the second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom".

Here's a reference for a more in-depth reading