Question

A physical quantity is measured and the result is
expressed as nu where u is the unit used and n is the
numerical value. If the result is expressed in various
units then .

Answer 1

I would start by stating that for any measurement, the unit value is arbitrary. For instance, you can measure distance in meters, inches, etc., so start with the expression:

nu = mv

where mv is the same measurement in different units. If you consider mv a constant, you can manipulate the above equation to get:

n = (mv)/u

which shows that n is proportional to 1/u.

Basically whenever you take a measurement, that larger the units you use, the smaller the number is going to be. 1 meter is 100 centimeters is 1000 millimeters.

Or

Let us take an example of mass ,suppose if a body has a mass of 20 kg . (In this 20 is the numerical value and kg is the unit) So if we decrease the size of the unit , Say kg to g then the numerical value will be 20000.
20 kg = 20000 g.

-If the size of the unit Kg will be increased from kg to Quintal then the numerical value will be 0.2 .

20 kg = 0.2 Quintal.

from this example we can say that if the unit is increasing then the numerical value is decreasing & if the unit is decreasing then the numerical value of is increasing.

∴ numerical value, n ∝ 1/u
Thus it is proved.