1.1.2 Exact and Approximate Results
A standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With Mathematica, however, you can often get exact results.
Mathematica gives an exact result for , even though it has 31 decimal digits.
In:= 2 ^ 100
You can tell Mathematica to give you an approximate numerical result, just as a calculator would, by ending your input with //N. The N stands for "numerical". It must be a capital letter. Section 2.1.3 will explain what the // means.
This gives an approximate numerical result.
In:= 2 ^ 100 //N
Mathematica can give results in terms of rational numbers.
In:= 1/3 + 2/7
//N always gives the approximate numerical result.
In:= 1/3 + 2/7 //N
Getting numerical approximations.
When you type in an integer like 7, Mathematica assumes that it is exact. If you type in a number like 4.5, with an explicit decimal point, Mathematica assumes that it is accurate only to a fixed number of decimal places.
This is taken to be an exact rational number, and reduced to its lowest terms.
Whenever you give a number with an explicit decimal point, Mathematica produces an approximate numerical result.
Here again, the presence of the decimal point makes Mathematica give you an approximate numerical result.
When any number in an arithmetic expression is given with an explicit decimal point, you get an approximate numerical result for the whole expression.
In:= 1. + 452/62