This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 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[1]:= 2 ^ 100 Out[1]= 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]:= 2 ^ 100 //N Out[2]= Mathematica can give results in terms of rational numbers. In[3]:= 1/3 + 2/7 Out[3]= //N always gives the approximate numerical result. In[4]:= 1/3 + 2/7 //N Out[4]= 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. In[5]:= 452/62 Out[5]= Whenever you give a number with an explicit decimal point, Mathematica produces an approximate numerical result. In[6]:= 452.3/62 Out[6]= Here again, the presence of the decimal point makes Mathematica give you an approximate numerical result. In[7]:= 452./62 Out[7]= 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[8]:= 1. + 452/62 Out[8]=