A physical quantity is measured and its value is found to be nu where n = numerical value and u = unit. Then which of the following relations is true

To understand the relationship between the numerical value and the unit of a measured physical quantity, let us analyze how physical measurements work.

Any physical quantity is represented by the product of its numerical value ($n$) and the unit chosen for the measurement ($u$). This can be written as:
$Q=nu$
where $Q$ is the actual magnitude of the physical quantity.

The actual magnitude of a physical quantity $Q$ is constant and does not change, regardless of the system of units used to measure it. For example, a length of 1 meter is the same as 100 centimeters.

Since $Q$ remains constant, we have:
$nu=\text{Constant}$
This implies that:
$n\propto \frac{1}{u}$

Thus, the numerical value $n$ is inversely proportional to the size of the unit $u$. A larger unit will result in a smaller numerical value, and a smaller unit will result in a larger numerical value.

Therefore, the correct relation is n ∝ 1/u.