File: gawk.info,  Node: Inexact representation,  Next: Comparing FP Values,  Up: Inexactness of computations

16.4.1.1 Many Numbers Cannot Be Represented Exactly
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So, before you start to write any code, you should think about what you
really want and what's really happening.  Consider the two numbers in
the following example:

     x = 0.875             # 1/2 + 1/4 + 1/8
     y = 0.425

   Unlike the number in 'y', the number stored in 'x' is exactly
representable in binary because it can be written as a finite sum of one
or more fractions whose denominators are all powers of two.  When 'gawk'
reads a floating-point number from program source, it automatically
rounds that number to whatever precision your machine supports.  If you
try to print the numeric content of a variable using an output format
string of '"%.17g"', it may not produce the same number as you assigned
to it:

     $ gawk 'BEGIN { x = 0.875; y = 0.425
     >               printf("%0.17g, %0.17g\n", x, y) }'
     -| 0.875, 0.42499999999999999

   Often the error is so small you do not even notice it, and if you do,
you can always specify how much precision you would like in your output.
Usually this is a format string like '"%.15g"', which, when used in the
previous example, produces an output identical to the input.