# Exact and Approximate Results

A standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With the Wolfram Language, however, you can often get exact results.

The Wolfram Language gives an exact result for , even though it has 31 decimal digits:
 In:= Out= You can tell the Wolfram Language 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 // means.

This gives an approximate numerical result:
 In:= Out= The Wolfram Language can give results in terms of rational numbers:
 In:= Out= //N always gives the approximate numerical result:
 In:= Out= expr//N give an approximate numerical value for expr

Getting numerical approximations.

When you type in an integer like 7, the Wolfram Language assumes that it is exact. If you type in a number like 4.5, with an explicit decimal point, the Wolfram Language 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:
 In:= Out= Whenever you give a number with an explicit decimal point, the Wolfram Language produces an approximate numerical result:
 In:= Out= Here again, the presence of the decimal point makes the Wolfram Language give you an approximate numerical result:
 In:= Out= 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:= Out= 