The earliest known uniform systems of weights and measures seem to have all been created sometime in the 3rd millennia BC among the ancient peoples of Egypt and Mesopotamia.
A typical measurement system would be based on the use of parts of the body and the natural surroundings as measuring instruments. Early Babylonian and Egyptian records indicate that length was first measured with the forearm, hand, or finger and that time was measured by the periods of the sun, moon, and other heavenly bodies.
For example, the cubit:

Even the carat, still used as a unit for gems (especially diamonds), was derived from the carob seed and have seen numerous changes. Nowadays as a standardization, One Carat= 200 milligrams, or 0.2 grams.
A brief comparisation of diamond size and carat

However, the numerous civilzations and their measurement systems created a problem: Too many system of measurements which invariably lead to confusion and in worse cases, chaos.
Just considering the Cubit, we've the Egyptian cubit and the Mesopotamian cubit for a start. There were several cubits of different magnitudes that were used. The common cubit was the length of the forearm from the elbow to the tip of the middle finger. It was divided into the span of the hand (one-half cubit), the palm or width of the hand (one sixth), and the digit or width of a finger (one twenty-fourth). But even this detailed definition created problems: Almost everyone had different lengths of fingers, forearms and elbows!
Other measures of length used in ancient times included in India: the dhanus (bow), the krosa (cry, or cow-call) and the jojana (stage) while the Romans and Greeks contributed the foot, unicae, inchs, mile, pace, Roman mile, furlongs, yards, gird and so on, adding to the confusion.
Looking at Units of mass: people had to sort through the confusion of the units of: the grain, pound, mina, shekel, talent, libra, troy pound, ounce, uncia, carat, carob, stone, quarter, hundredweight, tonnes, long tonne just for a start =) if they ever needed to do exchange or trade.
Among the mess, groups of scientists sought to unify a system of units for common usage throughout the world, and it was only in 1960 (yes, after centuries of confusion) during The 11th General Conference on Weights and Measures, we adopted the name Système International d'Unités (International System of Units, international abbreviation S.I.), for the recommended practical system of units of measurement which includes the base units of seven well defined units: the kilogram, metre, second, ampere, kelvin, mole and the
candela and as such, the S.I system of units is still currently adopted by people around the world today.
You can find more information about the S.I. units at:
Bureau International des Poids et Mesures at http://www.bipm.org/en/si/
For a more detailed explanation of how scientists proceeded to setting the S.I measurement system into practice, you can go to: http://www.bipm.org/en/si/history-si/
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