Chapter 5 sec 2

 The place value system or the positional system, is the placement of the symbols in a numeral determines the value of the symbols.

 The Babylonian ruins are almost 60 miles south of modern-day Baghdad. The civilization lasted from 2000 BC to about 600 BC.  They had a primitive place value system. Do you know what they based their number system on?

 This system first appeared around 3100 B.C. It is also credited as being the first known positional numeral system, in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base (ten, one hundred, one thousand, and so forth), making calculations difficult. positional numeral system  wikipedia

 The Babylonians, who were famous for their astronomical observations and calculations (aided by their invention of the abacus). They inherited from the Sumerian and also Akkadian civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units).BabyloniansabacusSumerian Akkadian

 The Babylonian system of mathematics was sexagesimal (base-60) numeral system. From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60×6) degrees in a circle. sexagesimalnumeral system  The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting has survived for 4000 years.

 The Babylonian system only used 3 symbols to do their mathematics.  We are only going to use one and ten.

 How would the Babylonians write larger numbers?  For example how about the number 70?, 234?, or 9,083?

 To represent a larger number, the Babylonians used several groups of these symbols, separated by spaces, and multiplied the value of these groups by increasing powers of 60.

 3x = = 230

 How about Hindu-Arabic to Babylonian?  Convert 14,759.  First you will have to /60 2, then the result will have to be divided by 60

 Board work

 Napier Rods  The eighth Baron of Merchiston, Scotland, was also an amateur theologian.  Reasoned that the Roman pope was the anti-Christ, and from studying the Bible’s Book of Revelation, he deduced that God would destroy the world by 1700.

 From his invention of the rods, help astronomers, scientist, and engineers shorten the time it took to do lengthy calculations. A noted mathematician Pierre de Laplace, 200 years later, said because of the rods, Napier had doubled the life of astronomers.