Numbers with negative exponents have a very small absolute value, regardless of the sign of the overall number, while those with positive exponents have very large absolute values. Thus -1.86×10¹⁰⁰ has a huge absolute value, while -3.283×10^-33 has a teeny absolute value. However, 3.283×10^-33 is actually larger than -1.86×10¹⁰⁰ because the first is positive while the second is negative.

In every computer system that represents and manipulates floating point numbers, the size of the exponent and the size of the mantissa are fixed, usually by the hardware. When great precision is needed, software packages, like the 'bc' calculator of UNIX, can be used. Of course, it is futile to try to represent some real numbers with infinite precision because it just can't be done! π is an example, so is 1/3, which is 0.33333333333333....

In the following discussion and examples, we will use only decimal numbers because they are easier to work with (at least as far as humans are concernd) But the same general principles apply in binary.