Further Examples: Precision

Here is an approximate real number.

In[1]:=

This gives the precision of the real number.

In[2]:=

Out[2]=

This evaluates attempting to get a result with precision .

In[3]:=

Out[3]=

The result has precision .

In[4]:=

Out[4]=

Mathematica treats as a machine-precision number.

In[5]:=

Out[5]=

This evaluates using machine-precision numbers.

In[6]:=

Out[6]=

This evaluates using 30-digit precision numbers.

In[7]:=

Out[7]=

In this case, the result has a precision slightly less than .

In[8]:=

Out[8]=

This evaluates trying to get a result with precision .

In[9]:=

Out[9]=

Now the result has precision 30.

In[10]:=

Out[10]=

If you give input as a machine number, N cannot give you high-precision output.

In[11]:=

Out[11]=

SetPrecision can be used to convert machine numbers to high-precision.

In[12]:=

Out[12]=

If you want an exact representation of , then you have to convert it explicitly.

In[13]:=

Out[13]=

In[14]:=