Here's why:
* Dimensions represent fundamental physical quantities: Length (L), mass (M), time (T), temperature (Θ), electric current (I), amount of substance (N), and luminous intensity (J) are the seven base dimensions used in physics. Every physical quantity can be expressed as a combination of these base dimensions.
* Units are specific ways of measuring those quantities: For example, meters (m) and feet (ft) are units for length, which has the dimension L.
* A unit without a dimension wouldn't make physical sense: If you had a unit without a corresponding dimension, it wouldn't relate to any fundamental physical property. How could you compare or combine such a unit with others?
Example: Think of a quantity like "number of apples." We can count apples, and we might use the unit "apples" to do so. However, "apples" doesn't represent a fundamental dimension. It's just a way of quantifying something that already has a dimension – we could also say "apples" have the dimension of "number" or "count."
In summary: All physical quantities have dimensions, and units are simply the chosen ways to express those quantities. There's no such thing as a unit without a corresponding dimension.
