Which one of the following pairs of units may not be added together, even after the appropriate unit conversions have been made? a. grams and milligrams
b. miles and kilometers
c. kilometers and kilograms
d. centimeters and yards

c. kilometers and kilograms

Explanation:

If two units represent different things, like for example grams and joules, where the first one is a unit for mass, and the second one a unit for energy we can not add them together. (

Let's analyze each one of the given options:

a: grams and milligrams

both grams and milligrams are units of mass, so after the appropriate unit conversions, we can add them.

b: miles and kilometers

Both are units for distance, after the appropriate unit conversions, we can add them.

c: kilometers and kilograms

"Kilometer" is a unit for distance, and "kilogram" a unit for mass, we can not add distance and mass, so these two can not be added together.

d: centimeters and yards

Both are units of distance,  after the appropriate unit conversions, we can add them.

Then the only one that we can not add together is option c:  kilometers and kilograms

The correct option is C (kilometers and kilograms).

Explanation:

UNITS is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature. The magnitude of a physical quantity is expressed as, Physical quantity = (numerical value) × (unit). There are six basic units of measurement which includes:

--> metre (m) - unit of length.

--> kilograms (kg) - unit of mass.

--> second (s) - unit of time.

--> ampere (A) - unit of electrical current.

--> kelvin (K) - unit of temperature and

--> mole (mol) - unit of the amount of substance.

Mass is the quantity of matter present in a body which is constant and is measured in KILOGRAMMES or GRAMS. While position is the distance and direction of an object from a particular reference point which is known to vary and is measured in METERS OR KILOMETRES.

From the above definition, KILOGRAMMES is used to measure the magnitude of a different quantity from KILOMETERS and therefore should not be added up after conversation.