1

Ancient Numeration Systems

Thank you Dr. Wyatt

2

Early man’s number concepts

one two

many

3

Egyptian Numeration1

10

100

1000

10,000

100,000

1,000,000

vertical staff

heel bone

coiled rope or scroll

lotus flower

pointing finger

fish

an astonished man

4

Roman numerals

• 1 I

• 10 X

• 100 C

• 1000 M

• 5 V

• 50 L

• 500 D

5

onesIIIIIIIVVVIVIIVIIIIXXXIXII

tensX

XXXXXXLL

LXLXX

LXXXXCC

CXCXX

hundredsC

CCCCCCDD

DCDCC

DCCCCMM

MCMCC

thousandsM

MMMMM

V

VII

IX

XI

6

The subtractive principle

I X C M

V L DI is only subtracted from V and X

X is only subtracted from L and C

C is only subtracted from D and M

7

Roman numerals ≥ 4000

IV4000

VI6000

XI11000

XX20,000

XIIICD13,400

XXVIIILX28,060

8

79

MDIII

404

CDXCV

9059

MMLXIX

7926

CMLXXXVII

Write the missing numeral

491

CCIX

862

DCCLXXIV

1095

CDXLVIII

2984

MCMXCII

CDXCI

209

DCCCLXII

774

MXCV

448

MMCMLXXXIV

1992

LXXIX

1503

CDIV

495

IXLIX

2069

VIICMXXVI

987

14

Mayan numerals

1

3

2

7

4

5

6

8

9

10

11

12

13

14

15

Mayan numerals23

24

25

1915

16

17

18

20

21

22 26

16

Counting by tens

1020

30

40

50

60

7080

90

100

110

120

17

How manythousands

How manyhundreds

How manytens

How manyones

10 x 10 x 10 10 x 10 10 1

How many20 x 18 x 20

How many18 x 20

How many20

How manyones

3 7 5 2 7200

360

20

1

18

Mayan numerals

37 69 13155

2 x 20

15 x 1

5 x 20

0 x 1

12 x 20

4 x 1

100 244

19

Mayan numerals

188 275 532334 939 1097

16 x 20

14 x 1

2 x 360

10 x 20

19 x 1

3 x 360

0 x 20

17 x 1

20

Babylonian Numeration

From 1 to 59, each number was written by the Babylonians with the same structure as the Egyptians wrote it.

14 =

32 =

55 =

21

Babylonian Numeration

61 =

64 =

72 =

96 =

60 =

22

151 =

250 =

383 =

674 =

2527 =

Babylonian Numeration

23

Review of numeration systems

24

419

CMLXVI

1890

MMDCIX

4095

IXXLVIII

7926

CMLXXXIV

Write the missing numeral

147

CDLXXXII

664

MCMVIII

937

MMDCLXXIV

7049

XDXC

CXLVII

482

DCLXIV

1908

CMXXXVII

2674

VIIXLIX

10,590

CDXIX

966

MDCCCXC

2609

IVXCV

9048

VIICMXXVI

984

25

Mayan numerals

83 345 1398191 911 1803

9 x 20

11 x 1

2 x 360

9 x 20

11 x 1

5 x 360

0 x 20

3 x 1

27

You can’t teach what

you don’t know any

more than you can

come back from

where you ain’t been.

- Will Rogers