Who Discovered Rational Numbers?

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The treatment of all numbers as rational is traced to Pythagoras, an ancient Greek mathematician. Pythagoras believed that any number could be expressed as a ratio of two integers, such as 3/4 or 5/10.

Rational numbers are used to express quantities or values that natural numbers or integers alone cannot, such as in measurement of length, mass or time. For example, a rational number can describe a fraction of a bushel of wheat that a farmer wants to sell.

However, Pythagoreans later discovered that not all numbers were rational. For instance, the square root of two, which is the length of the longer side of a triangle with sides one and one, is not a rational.