They are used in exactly the way with which you are familiar from arithmetic. Compare the results of the two multiplications. When Mathematica operates on rational numbers, it gives an exact result no matter how many digits are required. When Mathematica operates on two floating-point numbers, it gives the answer in scientific notation rounded to six decimal places. Again, notice that Mathematica gives exact results for the rational division and a result rounded to six digits for the floating-point division.
Exercises Compute the following values.
The difference between your height in feet and your best friend's height in feet. Compare the results of the following operations to the ones in the previous section. In each case, the result is the same as it would have been if both of the numbers had been floating-point numbers. We have been careful not to make any mistakes in our expressions to this point, but they will be very common when you experiment with Mathematica . Mistakes can be things like forgetting an operator symbol, forgetting a panthesis, putting in too many parentheses, and the like.