## Javascript rounding error

HI

There is a rounding error problem that I encountered using Java script.
The problem occurs when you do an caculation 4.225 times a integer:
Note ^ means exponent
I.e. 10^3 = 1000 and 10^2 = 100
Here are the output that Java script's caculation result

4.225 * 10 = 42.25
4.225 x 100 = 422.49999999999994
4.225 x 1000 = 4225
4.225 x 10000 = 42250
4.225 x 100000 = 422499.99999999994
4.225 x 10^6 = 4225000
4.225 x 10^7 = 42250000
4.225 x 10^8 = 422499999.99999994
....
4.225 x 10^11 = 422499999999.99993
....
4.225 x 10^14 = 422499999999999.93
...
4.225 x 10^17 = 422499999999999930
...
4.225 x 10^-2 = 0.042249999999999996
Note: There is no rounding error when 4.225 times a number that is smaller
than 0.01

It seems that when 4.225 x 10^X when X is a natural number and X is in the
expression of 2+3n (when n is a natural number) or X = -2 it will give you
a rounding error.

I know decimal number in most of the program langauge is represented by a
floating number which is a binary represetation.

I did some investigation on Java Script as well as the number 4.225 and here
is what I found
1. 4.225's hex(base 16) representation is 4.399999999999999999999999999....
which is a infinite decimal represtation (like 1/3)
2. Java script is typless and integer value can be from -2^53 to 2^53 ( I
think that means there are 54 bits are used to store both mantissa and exponent).

I thought the problem is when certain bits been taken away from mantissa
to exponent, there is some minor information that stored in mantissa been
lost, that's why we have a rounding error.

My question is:
1. How do we get around?
2. How do we "detect" those floating point problems give some "known" implemetation
about how the floating point been handled in certain program. ( I think there
is a general problem with floating point in some cases, 4.225 is just one
of those examples)