The Egyptians repeated a sign as many times as needed. The scribes of Mesopotamia and Chinese calculators gave a digit its value by its place.
The question
To write 9,999, do you need thirty-six signs, or just four?
What you do Choose a number, or start the counter. See how many signs Egypt needs, where symbols are added up, and how many places are needed when position gives the value.
Without JavaScript, here are the animation’s data.
| System | Principle | Source |
|---|---|---|
| Egypt | Additive, base 10: one sign for 1, for 10, for 100, for 1,000…, repeated as many times as needed | 1 |
| Mesopotamia | Positional, base 60: an empty place, long marked by a simple space | 2 |
| China (rods) | Positional, base 10: each column is worth ten times the next; an empty square for no value | 3 |
| Number | Egyptian signs | Places in base 60 | Columns on the board |
|---|---|---|---|
| 20 | 2 | 20 | 2 · 0 |
| 276 | 15 | 4 · 36 | 2 · 7 · 6 |
| 205 | 7 | 3 · 25 | 2 · empty · 5 |
| 3,601 | 10 | 1 · empty · 1 | 3 · 6 · empty · 1 |
| 9,999 | 36 | 2 · 46 · 39 | 9 · 9 · 9 · 9 |
The values in the second table are calculated. In the animation, the Egyptian signs are drawn in simplified form, and the base-60 places are written with our digits.
The takeaway In an additive system, the number of signs grows with the number. With place value, a few places are enough, but an empty place has to be marked.
Photo credits 6
- The Rhind Mathematical Papyrus, detail: Egyptian calculation problems (British Museum, EA 10057). Ahmes (scribe), Public domain, source
- Tablet YBC 7289, Old Babylonian period: a square, its diagonal and base-60 numbers giving an approximation of the square root of 2 (Yale Peabody Museum). A. Urcia, Yale Peabody Museum of Natural History, CC0, source
- Lead counting rods, Western Han period (National Museum of China; Xi’an, 1982). Gary Todd, CC0, source
- The Egyptian sign for ten (V20 in Gardiner’s list), drawn in the Abydos font. George Douros, Public domain, source
- The Egyptian sign for a hundred (V1 in Gardiner’s list), drawn in the Abydos font. George Douros, Public domain, source
- The Egyptian sign for a thousand (M12 in Gardiner’s list), drawn in the Abydos font. George Douros, Public domain, source
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Sources 3
O’Connor, John J. and Robertson, Edmund F., “Babylonian Numerals” et “Egyptian Numerals”, MacTutor History of Mathematics, University of St Andrews, “Egyptian numerals” (MacTutor), 4th paragraph (“The Egyptians had a bases 10 system…”) and 6th paragraph (“As can easily be seen…”).
The Egyptians had a bases 10 system of hieroglyphs for numerals. By this we mean that they has separate symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million. […] One just adds the individual symbols, but replacing ten copies of a symbol by a single symbol of the next higher value.
Open access open the source · checked on 24 October 2026
O’Connor, John J. and Robertson, Edmund F., “Babylonian Numerals”, example of tablet AO 17264.
Perhaps the scribe left a little more space than usual between the 6 and the 9
Open access open the source · checked on 27 October 2026
O’Connor, John J. and Robertson, Edmund F., “Chinese Numerals”, MacTutor History of Mathematics, University of St Andrews, January 2004, “Chinese numerals” article, part on the counting board.
A counting board consisted of a checker board with rows and columns. Numbers were represented by little rods made from bamboo or ivory. […] There was still no need for a zero on the counting board for a square was simply left blank.
Open access open the source · checked on 27 October 2026
Read the entry 9.1 · Counting: number systems around the world