In the SI system, how are base units and derived units related?

• A. Base units are formed by combining derived units through algebraic relationships.
• B. Derived units are defined only by adding base units together, without multiplication, division, or exponents.
• C. Derived units are formed by multiplying and/or dividing base units (and sometimes raising them to powers) to represent other physical quantities.
• D. Base units and derived units are unrelated; each physical quantity has a unique unit not connected to others.

Answer: (C)

Verified step by step guidance

1. Understand that in the SI system, base units are the fundamental units for physical quantities such as length, mass, time, electric current, temperature, amount of substance, and luminous intensity.
2. Recognize that derived units are constructed from these base units by using algebraic operations like multiplication, division, and exponentiation to express other physical quantities.
3. Recall that derived units can be represented as combinations of base units raised to various powers, for example, velocity has units of length divided by time, expressed as \(\mathrm{m \cdot s^{-1}}\).
4. Note that derived units are not formed by simply adding base units together; addition of units is not physically meaningful in this context.
5. Conclude that the relationship between base and derived units is that derived units are formed by multiplying and/or dividing base units (and sometimes raising them to powers) to represent other physical quantities.