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
gives an exact
, even though it has 31 decimal digits.
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. "Special Ways to Input Expressions"
will explain what the
This gives an approximate numerical result.
can give results in terms of rational numbers.
always gives the approximate numerical result.
|expr//N||give an approximate numerical value for expr|
Getting numerical approximations.
When you type in an integer like
assumes that it is exact. If you type in a number like
, 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.