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Egyptian numerals

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Egyptian numerals

The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a positional notation such as the decimal system. The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.[citation needed]

The following hieroglyphs were used to denote powers of ten:

Multiples of these values were expressed by repeating the symbol as many times as needed. For instance, a stone carving from Karnak shows the number 4,622 as:

Egyptian hieroglyphs could be written in both directions (and even vertically). In this example the symbols decrease in value from top to bottom and from left to right. On the original stone carving, it is right-to-left, and the signs are thus reversed.[citation needed]

There was no symbol or concept of zero as a placeholder in Egyptian numeration and zero was not used in calculations. However, the symbol nefer (nfr𓄤, "good", "complete", "beautiful") was apparently also used for two numeric purposes:

According to Carl Boyer, a deed from Edfu contained a "zero concept" replacing the magnitude in geometry.

Rational numbers could also be expressed, but only as sums of unit fractions, i.e., sums of reciprocals of positive integers, except for 23 and 34. The hieroglyph indicating a fraction looked like a mouth, which meant "part":

Fractions were written with this fractional solidus, i.e., the numerator 1, and the positive denominator below. Thus, 13 was written as:

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