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There are several reasons.
Measurement units evolved over time. People used different units across countries over time. Even now, you have the Imperial system that has been mostly abandoned by developed countries across the world. But USA, Burma, Liberia and a few Caribbean islands still use the Imperial system (or a variant).
Differences in scale: It would make little sense to measure the distance between two cities in metres, or the size of an ant. In the first case you would use a kilometre, in the second a millimetre.
Sometimes the way in which a physical measure is derived will affect its units. Energy can be defined as the ability to do work and so the unit is the same as the unit for work: a Joule. However, thermal energy is defined as the amount of heat required to raise the temperature of 1 gram of pure water by 1 kelvin and in 1 calorie.
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A fraction whose numerator and denominator represent the same quantity but use different units?
A unit conversion ratio
What does this definition mean A ratio of equivalent values used to express the same quantity in different units?
It could be the definition of equivalent ratios.
A fraction in which the numerator and denominator represent the same amount but are in different units?
What is a fraction in which the numerator and denominator represent the same amount but are in different units?
Is this true that conversion factor is a ratio of equivalent values used to express the same units in different quantities?
No. The same quantities in different units.
What does units agree mean?
In mathematics, two quantities are said to be in units agreement if they have the same units of measure. For example, if two quantities are both measured in meters, then they are in units agreement. If one quantity is measured in meters and the other is measured in centimeters, then they are not in units agreement.
