Sistema de numeración babilónico

SESO DEL IES LAS CUMBRES. GRAZALEMA MATEMÁTICAS 1º ESO
http://iesgrazalema.blogspot.com

SISTEMA DE NUMERACIÓN BABILÓNICO
· Babilonia – Asia: 1730 a. C. – 539 a. C.
· Sistema de numeración híbrido:
- Aditivo de base diez hasta el 60.
- Posicional para números superiores al 60.
· Dígitos:

1 10
· Ejemplos:
- Hasta el 60 → Aditivo

1 2 3

4 5 6

7 8 9

10 11 12 13

14

15 16

18 19

20 21

27 29
1

30

34

38

40 42 45 46

50 53

59

1 · 60 = 60 → Se escribe como el 1, pero con un mayor espacio entre él y los dígitos
siguientes.

- Para números superiores al 60 → Posicional

1 · 60 + 1 = 61 1 · 60 + 2 = 62

1 · 60 + 9 = 69

1 · 60 + 10 = 70 1 · 60 + 12 = 72

1 · 60 + 20 =80

1 · 60 + 25 = 85

2

1 · 60 + 30 = 90

1 · 60 + 38 = 98

1 · 60 + 40 = 100 1 · 60 + 43 = 143

1 · 60 + 50 = 110

1 · 60 + 59 = 119

2 · 60 = 120

2 · 60 + 1 = 121

2 · 60 + 59 = 179

3 · 60 = 180

3

239 60
59 3

239=3 59 (60=59 · 6003 · 601=59 · 13 ·60=3 ·6059

3 · 60 + 59 = 239
······························································································································································

240 60 ˙
240=60
00 4

240=4 0 (60=0· 600 4 · 601=0· 14 ·60=04 · 60=4 · 60

4 · 60 = 240
······························································································································································

599 60
59 9

599=9 59( 60=59 ·60 09 · 601=59 ·19 ·60=9 · 6059

9 · 60 + 59 = 599
······························································································································································

600 60 ˙
600=60
000 10
0

0 1
600=10 0(60=0 ·60 10 · 60 =0 · 110 · 60=010 · 60=10 · 60

10 · 60 = 600
4

2315 60
515 38
35

2.315=38 35( 60=35 ·60 038 ·60 1=35 ·138· 60=38· 6035

38 · 60 + 35 = 2.315
······························································································································································

7414 60
141 123 60
214 03 2
34

7.414=2 3 34 (60=34· 600 3· 601 2 ·60 2=34 · 13 · 602· 3.600=2 · 3.6003 ·6034

2 · 3.600 + 3 · 60 + 34 = 7.414
······························································································································································

32415 60
241 540 60
015 00 9
15

0 1 2
32.415=9 0 15( 60=15· 60 0 · 60 9 · 60 =15 · 10 · 609· 3.600=9 ·3.6000 · 6015
Para evitar confusiones, introdujeron un signo separador cuando
el valor de un orden intermedio era cero.

9 · 3.600 + 0 · 60 + 15 = 32.415
5

79346 60
193 1322 60
134 122 22
146 02
26

79.346=22 2 26 (60=26· 60 02 · 60122· 60 2=26 · 12· 6022 · 3.600

22 · 3.600 + 2 · 60 + 26 = 79.346
······························································································································································
148312 60
283 2471 60
431 071 41
112 11
52

0 1 2
148.312=41 11 52( 60=52 ·60 11 ·60 44 · 60 =52 ·111 · 6041 ·3.600

41 · 3.600 + 11 · 60 + 52 = 148.312
······························································································································································
725642 60
125 12094 60
0564 0094 201 60
242 34 21 3
02

725.642=3 21 34 2(60=2 ·60 034 · 60121· 60 23 ·60 3 =
= 2 ·134 ·6021· 3.6003· 216.000=3 · 216.00021· 3.60034 · 602

3· 216.000 + 21 · 3.600 + 21 · 3.600 + 2 = 725.642

6

Sistema de numeración babilónico

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