In[2]:= Pi

Out[2]= Pi

In[3]:= N[Pi]

Out[3]= 3.141592653589793

In[4]:= Pi100 = N[Pi, 100]

Out[4]= 3.1415926535897932384626433832795028841971693993751058209749445923078\
   164062862089986280348253421170680

In[5]:= N[Pi,200]

Out[5]= 3.1415926535897932384626433832795028841971693993751058209749445923078\
   16406286208998628034825342117067982148086513282306647093844609550582231725\
   35940812848111745028410270193852110555964462294895493038196

In[6]:= N[Pi100,200]

Out[6]= 3.1415926535897932384626433832795028841971693993751058209749445923078\
   164062862089986280348253421170680

   If you try N[Pi] on the terminal line, you do not get as many
digits of precision as shown in these examples.  If you want the
full precision, use the following command (which changes the format
of stdout data from "OutputForm" to "InputForm".

In[8]:= SetOptions [ "stdout", FormatType -> InputForm ]

Out[8]= {FormatType -> InputForm, PageWidth -> 78, PageHeight -> 22, 
   TotalWidth -> DirectedInfinity[1], TotalHeight -> DirectedInfinity[1], 
   StringConversion :> $StringConversion}

In[9]:= N[Pi]

Out[9]= 3.141592653589793   (On a terminal, Out[3] will look different!]

In[10]:= NIntegrate[ 1/Sqrt[x], {x,0,1} ]

Out[10]= 2.000000000016163



   The about calculation used the default machine precision since
all inputs used the machine precision.  To get more internal
precision, use the "WorkingPrecision" option.  (This fails to
get the default 20 digits of desired precision in the interal, so
we have to retry with a lower PrecisionGoal value.)

In[11]:= NIntegrate[ 1/Sqrt[x], {x,0,1}, WorkingPrecision->30]

NIntegrate::ncvb: 
   NIntegrate failed to converge to prescribed accuracy after 7
     recursive bisections in x near x = 4.36999 10^(-57)   .

Out[11]= 2.00000000000000000000

In[12]:= NIntegrate[ 1/Sqrt[x], {x,0,1}, WorkingPrecision->30,
				 PrecisionGoal->19 ]

Out[12]= 2.00000000000000000000