Take a look in your Numerical Methods text, or
google for "floatingpoint number" mantissa, you'll get pages like read this.
Basically, a floating point number consists of two portions:
- The exponent determines the magnitude you can represent, how large or small a number can be. Can we represent the grains of sand in a sphere the size of the earth? in a sphere the size of the solar sytem? Can we approximate the number of electrons in a mile? in a light year? in a cubic parsec?
- The mantissa specifies how precisely those numbers can be specified. Can you state the national deebt to the penny or only plus or minus a million? When you make a recipe, do you use a cup of water? or 1.0000 cups? Floating point numbers have a finite number of bits to represent the value. but if you are trying to represent 1.00 you might be off by as much as +/- 0.005 ... but trying to represent 1.00 * 10^6 your error boils down to +/- 5000. But in either case, you're within half a percent.
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