Babylonian MathsBabylonian Maths

Numbers in base 60

• What do you think these five numbers are?

• What do you think these five numbers are?

20

• What do you think these five numbers are?

20

40

• What do you think these five numbers are?

2053

40

• What do you think these five numbers are?

20

28

5340

• What do you think these five numbers are?

20

4928

5340

In base 60 …In base 60 …

• Any number between 1 and 60 corresponds to the units in our numbers.

• Getting to 60 in base 60 is like getting to 10 in base 10.

• We don’t need a new symbol when we get to 10, and the Babylonians didn’t need a new symbol for 60.

• What do you think these three numbers are?

60 + 10 60 + 20 120 + 10= 70 = 80 = 130

• What do you think these two numbers are?

2 x 60 + 13 3 x 60 + 28= 133 = 208

Writing numbers in Writing numbers in base 60base 60• You don’t have to write base 60

numbers in cuneiform symbols.• Look at these base 60 numbers – can

you work out what they mean?

• Can you change these base 10 numbers into base 60?

Base 60

0 18

1 39 3 06 11 20

Base 10

18 60 + 39 = 99

180 + 6 = 186

660 + 20 = 680

Base 10

29 69 149 299

Base 60

29 1 09 2 29 4 59

ZeroZero

• The Babylonians didn’t have a separate symbol for 0.

• This number would have meant

3600 + 1 = 3601

• The zero lots of 60 would have just been a gap.

• Is this a good way of showing a zero, do you think?