Egyptian numerals

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The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BCE[1] until the early first millennium CE. 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 place-valued system such as the decimal system.[2] The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.[citation needed]

Digits and numbers[]

The following hieroglyphs were used to denote powers of ten:

Value 1 10 100 1,000 10,000 100,000 1 million, or
many
Hieroglyph
Z1
V20
V1
M12
D50
I8
C11
Gardiner's sign list ID Z1 V20 V1 M12 D50 I8 C11
Description Single stroke Cattle hobble Coil of rope Water lily
(also called lotus)
Bent finger Tadpole Heh[3]

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 4622 as:

M12M12M12M12
V1 V1 V1
V1 V1 V1
V20V20Z1Z1

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]

Zero and negative numbers[]

nfr
 
heart with trachea
beautiful, pleasant, good
F35

By 1740 BCE, the Egyptians had a symbol for zero in accounting texts. The symbol nfr (