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The US system that is based on the number 10 is the base 10 system. In the base 10 system the numbers roll over every 10; example 10,20,30.
That system is called the Arabic System. It was invented by the Hindus, adopted by the Persians, and passed to the Arabs.
The base of our number system is 10. However there are mathematical methods of converting bases to 2 , 5 ...e.t.c.
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