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Egyptians developed the first known use of fractions. They looked similar to our modern style of writing them, with one number over another, but their discovery was limited, as they could only use the number 1 in the numerator.
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Indian mathematicians developed the number zero as a placeholder, for when a "column" (e.g. tens column, hundreds column, etc.) has no value.
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Similar to how our culture counts using our fingers, Mayans counted using their fingers and toes. Thus, the Mayan counting system was base 20, rather than our base 10.
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Indian Mathematicians introduced the Hindu-Arabic numerals to European mathematicians, and Europe quickly adopted them as their own.
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Leibniz invented binary code, which is a base 2 counting system.
Later in history, this system would become very important as computers began to be developed. Because the system only consists of ones and zeros, computers can read these as "on" or "off".