Ancient Numeration Systems used for Math

1. Numeration
Systems
Past & Present

2. Egyptian System
This is one of the earliest recorded numeration systems based on
hieroglyphs dating back to 3400 B.C.

3. Example
125 was written as
336 was written as

4. Babylonian System
Babylonian mathematics used a base 60, numeric
system, which could be counted physically using
the twelve knuckles on one hand the five fingers on
the other hand.
Babylonian were the first to have a true place-
value system, where digits written in the left
column represented larger values,
Babylonian advances in mathematics were
probably facilitated by the fact that 60 has many
divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60).
Additionally, 60 is the smallest integer divisible by
all integers from 1 to 6.
We see continued modern-day usage of the
Babylonian system in 60 seconds in a minute, 60
minutes in an hour, and 360 (60 x 6) degrees in a
circle.

5. BABYLONIAN NUMERATION SYSTEM
Two symbols and their equivalents:
= 1
= 10
5482 =

6. Roman System

7. Use of Subtraction
4 IV 9 IX
40 XL 90 XC
400 CD 900 CM

8. Example
1959 was originally written
1959 was with the subtractive principle as

9. Mayan System
Mayan Numeral Modern
Equivalent
Shell
0
Pebble 1
Stick 5
The Mayan numeration system used three symbols, a pebble, a stick and a
shell. This system is based on the Mayan calendar which had 18 months and
each month had 20 days.

10. MAYAN NUMERATION SYSTEM

11. Numbers larger than 20
Numeral times Place Value
Place Value
360
20
1
Numeral
8
1
0

12. Example