Hi Raabi;

Generally to get higher precision you will need to work with higher precision.

Well a program should behave what its programmed for. If it's programmed to use  Newton's method, it will  and its the same what you do on paper. But at the same time computers have limitations. In this case the limitation is on decimal points ,computers work only with binary numbers they don't understand decimal points they don’t even understand negative numbers
in binary we can only have positive whole numbers {0,1,2,...} and even whole numbers are limited ,the range will depend on the bits you are using to describe the number.

So how come we can calculate decimal and negative stuff on our computers?
Computers use a special format to represent decimal points, normally in the world of programming we say floating point numbers for decimal point numbers ex .. {0.25,0.55,...}.It is important to know that binary floating point system can only represent a finite number of floating point numbers in exact form, its because the number of bits used to represent the  floating point system, if you exceed that limit then you will loose the precision.

http://en.wikipedia.org/wiki/Floating_point

You have to need programming knowledge to understand these...

If you want to know more about this format search "Floating-Point " IEEE is the most commonly used format.

Here is an example floating point numbers and their precision on my 32bits computer programmed in a C++ compiler with ANSI/ISO C++ standards
float type data gives 6 digit precision.
double type data gives 10 digit precision.

Good Luck

Last edited by debjit625 (2012-11-24 04:24:20)

Thanks Bobbym. I got some hint. Some people, like myself, are not good at asking their questions well - I'll try to improve.

Is it one of the main reasons for using Numerical methods, called improved Approximation?

I have some idea on Single Precision & Double Precision Floating Point numbers; but still could not understand; why should we use Numerical methods for the problems; which can be solved with plain algebra (probably called Analytical methods?). A real life example; comparing the two methods may resolve my problem for ever.

I am afraid, you people may feel off for my too basic questions. I can request to bear with me just for a little while; until I start walking, from crawling, on the path of you geeks. Thanks.

I see! We are actually getting redied for a bigger altar.  It is time to run away :-) Thank you Bobbym and have a good time.