Because that would lead to circular definitions.
Because.... There are two types of physical quantities. Fundamental and derived. Fundamental units cannot be derived from any of the two types of units while derived units can be derived from these two types of units. It's important to be clearly defined as there are so many indices of the base number. And no one can derive the units if they aren't properly defined
Yes, scalar quantities can be added, as long as they are the same dimension and you keep units straight. For example you cannot add cubic meters to square meters. But (especially in the imperial system) pounds and ounces, or feet and inches are added, and displayed in that fashion. Minutes and seconds is another.
Scalar - a variable quantity that cannot be resolved into components. Most of the physical quantities encountered in physics are either scalar or vector quantities. A scalar quantity is defined as a quantity that has magnitude only. Typical examples of scalar quantities are time, speed, temperature, and volume. A scalar quantity or parameter has no directional component, only magnitude. For example, the units for time represent an amount of time only and tell nothing of direction. Vector - a variable quantity that can be resolved into components. A vectorquantity is defined as a quantity that has both magnitude and direction. To work with vector quantities, one must know the method for representing these quantities. Magnitude, or "size" of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis.
Scalar - a variable quantity that cannot be resolved into components. Most of the physical quantities encountered in physics are either scalar or vector quantities. A scalar quantity is defined as a quantity that has magnitude only. Typical examples of scalar quantities are time, speed, temperature, and volume. A scalar quantity or parameter has no directional component, only magnitude. For example, the units for time represent an amount of time only and tell nothing of direction. Vector - a variable quantity that can be resolved into components. A vectorquantity is defined as a quantity that has both magnitude and direction. To work with vector quantities, one must know the method for representing these quantities. Magnitude, or "size" of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis.
Basic or fundamental quantities are seven in number. They cannot be derived right from one another. Hence they are independent. They are length, mass, time, electric current, temperature, quantity of substance, luminosity. Two sub are there. They are plane angle and solid angle. But derived are many in number. Just by the name they are derived right from the fundamental. They are area, volume, velocity, acceleration, force, momentum, magnetic induction, electric field, dipole moment, pressure, density etc etc
Those quantities which cannot be derived from any other such as length, mass, time, temperature, electric current, light luminosity are examples for fundamental physical quantities.
The quantity which has only direction is called fundamental quantity.Example-Direct current.The quantity which has both magnitude and direction is called derived quantity.Example-Altranating current.
The quantity of arithmetic cannot be measured and so the density is not defined.
Basic or fundamental quantities are seven in number. They cannot be derived right from one another. Hence they are independent. They are length, mass, time, electric current, temperature, quantity of substance, luminosity. Two sub are there. They are plane angle and solid angle. But derived are many in number. Just by the name they are derived right from the fundamental. They are area, volume, velocity, acceleration, force, momentum, magnetic induction, electric field, dipole moment, pressure, density etc etc
Temperature is a fundamental quantity itself, like length, mass and time. You cannot relate it in this way.
Mass is a scalar quantity. Scalar quantities are those characteristics of matter that can be measured with a scale, while vector quantities are those that involve direction as well as quantity.
Those quantities which cannot be derived from any other such as length, mass, time, temperature, electric current, light luminosity are examples for fundamental physical quantities.