4.137e12we can be off by as much as
0.0005e12 5.000 e8or $5 hundred million.
But the accuracy is dependent on the value of the exponent. For example, the number of people in this course is
8.300e 1which is off at most by
0.0005e 1 5.000 e-3or only 0.005 people.
In both of these cases we have 4 digits of precision, but vastly different accuracy in the representation.
So we see that the limited number of digits affects the precision and accuracy with which we can store numbers in the computer. In addition, because of this limitation, performing arithmetic operations can affect the accuracy of the result.
For example, consider:
However, all is not lost. There are techniques to iteratively compute more complicated functions such as sin, cos, etc., and manitain a desired accuracy.