Excel and almost every other computer program maintain decimal (base 10)
numbers in binary (base 2) floating point. Binary (base 2) has two numbers,
0 and 1, which is what computers understand. If a base 10 number is an
integer, it can be represented exactly in base 2. However if it has a
decimal fraction, many times it can only be approximated in base 2. For
example, 0.1 and 0.4 can be represented only approximately in base 2 whereas
0.5 can be represented exactly. To see how a base 10 number is represented
in base 2, 32 bit and 64 bit floating point, see:
http://babbage.cs.qc.edu/IEEE-754/Decimal.html This allows you to enter a
decimal number, see its base 2 representation and see the resultant decimal
number. For example 77.1 decimal after conversion to base 2, 32 bit floating
point, and back to base 10 is 77.099998.
