What is a numeral?
A numeral is a standard symbol for a number. For example, X is the Roman numeral
that corresponds to 10 in the standard Hindu-Arabic system.What were the two fundamental ideasin the development of numerical symbols?
There were two basic principles in the development of numerical symbols: First, a cer-
tain standard sign for the unit is repeated over and over, with each sign representing
the number of units. For example, III is considered 3 in Roman numerals (see the
Greek and Roman Mathematics section below for an explanation of Roman numerals).
In the other principle, each number has its own distinct symbol. For example, “7” is the
symbol that represents seven units in the standard Hindu-Arabic numerals. (See below
for an explanation of Hindu-Arabic numbers; for more information, see “Math Basics.”)MESOPOTAMIAN NUMBERS
AND MATHEMATICS
What was the Sumerian oral counting system?
The Sumerians—whose origins are debated, but who eventually settled in
6 Mesopotamia—used base 60 in their oral counting method. Because it required the
What are the names of the various base systems?
T
he base 10 system is often referred to as the decimal system. The base 60 sys-
tem is called the sexagesimal system. (This should not be confused with the
sexadecimal system—also called the hexadecimal system—or the digital system
based on powers of 16.) A sexagesimal counting tableis used to convert num-
bers using the 60 system into decimals, such as minutes and seconds.The following table lists the common bases and corresponding number systems:Base Number System
2 binary 9 nonary
3 ternary 10 decimal
4 quaternary 11 undenary
5 quinary 12 duodecimal
6 senary 16 hexadecimal
7 septenary 20 vigesimal
8 octal 60 sexagesimal