Mathematics Throughout History

Development Ofweights and Measures

What was the first civilization to use
a decimal system of weights and measures?

Between 2500 and 1700 B.C.E., the Harappa (or Harappan) civilization of the Punjab—now a province in Pakistan—developed the earliest known decimal system of weights and measures (for more about decimals, see “Math Basics”). The proof was first found in the modern Punjab region, where cubical (some say hexahedral) weights in graduated sizes were uncovered at Harappa excavations.

Archeologists believe that these weights were used as a standard Harappan weight system, represented by the ratio 1 : 2 : 4 : 8 : 16 : 32 : 64. The small weights have been found in many of the regional settlements, and were probably used for trade and/or collecting taxes. The smallest weight is 0.8375 grams (0.00185 pounds), or as measured by the Harappa, 0.8525; the most common weight is approximately 13.4 grams (0.02954 pounds), or in Harappa, 13.64, the 16th ratio. Some larger weights represent a decimal increase, or 100 times the most common weight (the 16th ratio). Other weights correspond to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500.

There is also evidence that the Harappan civilization had some of the most advanced length measurements of the time. For example, a bronze rod found at an excavation was marked in units of precisely 0.367 inch (0.93 centimeter). Such a measuring stick was perfect to plan roads, to construct drains for the cities, and even to build homes. An ivory scale found at Lothal, once occupied by the Harappan civilization, is the smallest division ever recorded on any measuring stick yet found from the Bronze Age, with each division approximately 0.06709 inch (0.1704 centimeter) apart.


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