[llevrok]

I often think about the trial and error that must have taken place. Countless attempts with no mechanical aid. Just sweat and effort!!

"What are you doing at work today, Fred?"
"I've had this idea in the back of my mind for something called a zero. I might give it a go now that I have a new stick".

[Lonesome in Massachussets]

The Babylonians used base-60 weighted place numbers. They did not have a sexagesimal point or a zero, so the order of sexagesimal magnitude had to be inferred. They left a space to show a zero, and understood how to express sexagesimal fractions. They knew how to divide by multiplying by sexagesimal fractions and some cuneiform tablets actually contain multiplication tables representing fractions that were not factors of 60, like 7 or 11. Dividing by 2, 3, 4, 5,6, 8 (repeated 2’s), 9, 10, or 12 is easy base 60. For instance a multiplication table was found showing multiplication by

142857 = (1,000,000/7)
285714 = (2,000,000/7)
428571 = (3,000,000/7)
571428 = (4,000,000/7)
714285 = (5,000,000/7)
857142 = (6,000,000/7)