Question

The numerical value of a measurement is:
A. directly proportional to the unit
B. inversely proportional to the unit
C. both
D. none

Answer 1

Hint
The numerical value along with its unit makes the measurement of a quantity. The relation between two different units for the same quantity will tell us the relation between the unit and its numerical value. With the help of units of the measurement like kg, litre, etc, the relation between the numerical value and its unit can be found out easily.

Complete step by step answer
It is better to know the definitions of the terms that we are going to use in further explanation. The definitions of measurement and the unit are as follows.
The measurement is the assignment of the number to the characteristics of the materials, objects, events, etc. The physical quantities are measured with respect to a fixed quantity called the unit.
Consider, for example, $x$ represents the magnitude and $y$ represents the unit. Thus, the overall expression is represented as follows.
$xy = {\text{constant}}$
Dividing both sides by we get,
$x = \dfrac{{{\text{constant}}}}{y}$
Let us consider a numerical example for a better understanding of the concept. An object has a mass of 10 kg. Here, 10 kg represents the physical quantity of an object. You may notice that 10 kg value can be converted to the other unit.
We know that $1g = 0.001kg$
Thus,
$10kg = 10,000g$
We also know that $1\,ton = \,1,000\,kg$
Thus,
$10\,kg = \,0.001\,ton$
Finally, we can conclude that,
$10,000\,g = 10\,kg = \,0.001\,ton$
From the above expression we get,
$\Rightarrow 10,000 > 10 > \,0.001\,$ …… (1)
Now ,consider the units,
$\Rightarrow gram\, < \,kg\, < \,ton$ …… (2)
Upon comparing the equations (1) and (2) we can notice that, as the numerical value decreases, the unit increases. Thus, both are inversely proportional to each other.
$\therefore$ The numerical value of a measurement is inversely proportional to the unit. Thus, option (B) is correct.

Note
We can say that, for a larger numerical value, the unit associated will be smaller and vice - versa. Some of the physical quantities do not have units, as they are the ratios of the physical quantities having the same units. For example, the strain is a unitless quantity, as it is a ratio of original to the extended length, and as the length of both is same, thus, the unit gets cancelled.