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### Babylonian Numbers

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Date: 11/17/1999 at 14:17:20
From: Kelley Phillips
Subject: Information on Babylonian Numbers

Our class is doing projects on many different number systems. I'm
doing the Babylonian system. Can you give me any information?

Thank you,
Kelley Phillips
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```
Date: 11/17/1999 at 15:25:07
From: Doctor Ameis
Subject: Re: Information on Babylonian Numbers

Hi Kelly,

An interesting question that has a large answer. Let me give you some
information about the Babylonian system (also called the Sumerian or
Mesopotamian system). You could use these various names to search the

The Babylonian system is sometimes called cuneiform writing. They used
a symbol sort of like a "Y" for one, and a symbol sort of like  <  for
ten. The symbols were made by pushing a pointed stick into wet clay.
When the clay dried they had a hard tablet that was something like a
"paper" copy of what they wrote.

There were several kinds of Babylonian numbers, but I will only talk
about one kind that used the symbols  Y  and  <  combined in ways such
as:

<YYY     and     <<<
YYY              <

The lefthand arrangement (number) has one 10-symbol and six 1-symbols
for a total of 16, and the righthand arrangement (number) has four
10-symbols for a total of 40. So far you can see that these numbers
take up a lot of space, but otherwise this system seems fairly
predictable. But wait...

Instead of using powers of 10 as we do for the place value positions,
they used powers of 60 (60, 3600, and so on.) This is similar to the
way we count seconds and minutes of time. We count 14 min. 58 sec.,
14 min. 59 sec., 15 min., 15 min. 1 sec., etc. Also we count minutes
up to 59 minutes and then add on another hour. They did this for all
their counting numbers.

Here is an example. 100, which equals 60 + 40, is 1 sixty and 40 ones.
We put a 1 in the sixties place and 40 in the ones or units place.
This is what 100 looks like in Babylonian:

Y  <<<
<

To figure out 1000 we first need to re-write it as 16 x 60 + 40 x 1,
which you should check yourself. This means 1000 is 16 sixties and 40
ones. This is what 1000 looks like in Babylonian.

<YYY  <<<
YYY   <

If this seems strange, keep in mind that it is not much stranger than
saying 16 minutes 40 seconds instead of 1000 seconds.

The Babylonian system did not have fractions in the way that we do.
Instead, parts of a whole (fractions) were written in a decimal way.
This is just like us writing .5 (a decimal) for the fraction 1/2.

Hope this helps. Let me know if you need more help.

- Doctor Ameis, The Math Forum
http://mathforum.org/dr.math/
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