Early Counting◦ Tokens◦ Tallies

Early Counting Methods

Plain Counting Tokens

Counting Tokens

Ishango Bone

Tally of the Exchequer

Inca Quipu

Number Bases◦ Quinary◦ Decimal◦ Duodecimal◦ Vigesimal◦ Sexagesimal

Base Number Systems

Egyptian Numerals

Egyptian Example

Babylonian Numerals

Cuneiform Tablet

Mayan Numerals

Greek Numerals

I=1 V=5 X=10 L=50 C=100 D=500 M=1000

Roman Numerals

IV=4 IX=9 XL=40 XC=90 CD=400 CM=900

Only symbols that are powers of 10 can be subtracted, and only from the next two largest values.

Roman Numerals: Subtraction