CIS3355: Business Data Structures
Fall, 2008
 

How do we deal with issues of magnitude?

As a review, remember that we defined magnitude as:

Magnitude. How large do we want our numbers to be?

Sometimes, we need to work with very large numbers. For example:

1.  The average human body contains roughly 7×10²⁷ atoms
2.  There are about 10⁴⁷ molecules of water on Earth
3.  The largest known prime number (has an order of magnitude of) 10^7,816,229

Notice these are very large numbers. Notice also that when we get to numbers this large, we tend to express them in scientific notation. Notice also that when we discuss number this large, we usually refer to them in terms of 'about' or approximately. Or goal usually is NOT precision (as is our concern with the mantissa), just approximation.

That is why, when we talked about the components we wanted to store, we represented the number we wanted to store as:

THE CHARACTERISTIC OF THE EXPONENT, is the value that we need to store, because it tells us how many places we need to move our decimal point (from it's normalized position, and in what direction we need to move it.) For example, we know that we could rewrite -567.678 as:

The characteristic of the exponent indicates what direction (+ to the right; - to the left) and how many (above, +3 means three digits to the right or -.56478 E+3 equates to -564.78). Let's take a look at a few more examples: