some simple numerical programs perhaps because most people have ten fingerswe seem to like to use decimals to represent numbers on the other handall modern computer systems represent numbers in binary this is not because computers are born with two fingers it is because it is easy to build hardware switchesi devices that can be in only one of two stateson or off that the computer uses binary representation and people decimal representation can lead to occasional cognitive dissonance in almost modern programming languages non-integer numbers are implemented using representation called floating point for the momentlet' pretend that the internal representation is in decimal we would represent number as pair of integers--the significant digits of the number and an exponent for examplethe number would be represented as the pair ( - )which stands for the product - the number of significant digits determines the precision with which numbers can be represented if for examplethere were only two significant digitsthe number could not be represented exactly it would have to be converted to some approximation of in this case that approximation is called the rounded value modern computers use binarynot decimalrepresentations we represent the significant digits and exponents in binary rather than decimal and raise rather than to the exponent for examplethe number ( / would be represented as the pair ( - )because / is in binary and - is the binary representation of - the pair ( - stands for - / what about the decimal fraction / which we write in python as the best we can do with four significant binary digits is ( - this is equivalent to / if we had five significant binary digitswe would represent as ( - )which is equivalent to / how many significant digits would we need to get an exact floating point representation of an infinite number of digitsthere do not exist integers sig and exp such that sig -exp equals so no matter how many bits python (or any other languagechooses to use to represent floating point numbersit will be able to represent only an approximation to in most python implementationsthere are bits of precision available for floating point numbersso the significant digits stored for the decimal number will be this is equivalent to the decimal number pretty close to / but not exactly /