Learn Decimal Numbers - Fast
Decimal numbers or "decimals" are not a new type of number, they are just a method of representing a number.
There are many methods of representing numbers, it's just that the decimal representation is frequently used in everyday life.
So how does it work?
It's easy, decimal representation is a base 10 representation, meaning a decimal number such as 39.684 is just shorthand for this..
39.684=3*(100)+9*(10)+6*(1/10)+8*(1/100)+4*(1/1000)
For a "recurring decimal" such as 1/3=0.3333.. the series just continues forever, like this..
1/3=0*(10)+3*(1/10)+3*(1/100)+3*(1/1000)+3*(1/10000)+..
Some people get confused and think that because irrational numbers are decimals that continue forever then any recurring decimal must be irrational. This is not true, as the simple example above shows, 1/3 is certainly rational, but in decimal notation it's a recurring decimal.
It's very tempting to assume that decimal representation is popular because it's base 10 and we have 10 fingers. It's tempting to assume base 10 must have been used forever. This is not true. The Babylonian Empire (1830-1531 BC) used base 60 and the legacy of this remains even today.. 60 minutes in an hour, 60 seconds in a minute.
Base 60 was used thousands of years before base 10, human fingers notwithstanding!
Clay tablets from the Babylonian Empire show a developed mathematics that knew about fractions, algebra, quadratic equations, cubic equations and pythagorean triplets roughly 1,000 years before Pythagoras.
Content written and posted by Ken Abbott abbottsystems@gmail.com