Egyptian numerals

The Egyptian numeral system was a way of counting used in Ancient Egypt. It was used from around 300 BC until the early first millennium AD. This system was based on multiples of ten. However, it did not use positional notation. In our modern decimal system, the position of a digit tells us its value. In Egypt, the value of a symbol was fixed regardless of where it was placed.

To represent larger numbers, the Egyptians repeated specific hieroglyphs. Each symbol represented a power of ten, such as one, ten, or one hundred. If a person needed to write a larger amount, they simply drew the symbol many times. For example, a stone carving found at Karnak shows the number 4,622. To create this, they used the symbol for one thousand four times. They also used the symbol for one hundred six times. They used the symbol for ten twice and the symbol for one twice.

Writing these numbers allowed for great flexibility in direction. Hieroglyphs could be written horizontally or vertically. They could also be written from left to right or right to left. In the Karnak example, the symbols decrease in value from top to bottom. They also decrease in value from left to right. On the original stone carving, the signs were reversed because it was written right to left. This shows how much variety existed in ancient writing styles.

One interesting feature of this system was the absence of a zero. The Egyptians had no symbol for zero to use as a placeholder. They also did not use zero in their mathematical calculations. However, they did use a word called nefer, which means "good," "complete," or "beautiful." This symbol served specific purposes in different contexts. In a papyrus listing court expenses, nefer indicated a zero balance. In drawings for the Meidum Pyramid, it indicated the ground level.

Because of nefer, Egyptians could describe measurements relative to a starting point. They measured height as being "above nefer." They measured depth as being "below nefer." The scholar Carl Boyer noted that a deed from Edfu contained a "zero concept." In this case, nefer replaced the magnitude in geometry. This shows how the idea of nothingness was handled without a formal zero digit.

When dealing with parts of a whole, the Egyptians used fractions. They expressed rational numbers as sums of unit fractions. A unit fraction is a reciprocal of a positive integer, like one-third or one-fifth. They used a specific hieroglyph that looked like a mouth to mean "part." This mouth symbol acted as a fractional solidus. To write a fraction, they placed the mouth over the denominator. They had special symbols for the fractions one-half and two-thirds.

While hieroglyphs were used for stone carvings, most daily work used hieratic script. Hieratic was written on papyrus or ostraca for administration and accounting. The hieratic system was much more efficient than standard hieroglyphs. The scholar Carl Boyer proved that hieratic used a different system. It used individual signs for numbers 1 through 9. It also had single signs for multiples of ten, hundreds, and thousands.

This efficiency made large numbers much easier to write in hieratic. For example, the number 9,999 required only four signs. In the hieroglyphic system, that same number would require 36 symbols. Boyer discovered that these hieratic numerals were ciphered. They mapped one number onto one Egyptian letter. This was a major development in human history. The Greeks eventually adopted this system for their own counting.