Printing π


π is wonderful when served Texas style! 
Remember the Á la mode!!


Simply to print an approximation to π to many digits can be a major problem.  A single line printed on ordinary paper can display 100 digits.  A page of 50 lines will then contain 5,000 digits.  Printing on both sides, each sheet of paper can hold 10,000 digits.

A ream of 500 sheets is approximately 5 cm thick.

The table then gives the approximate thickness of paper needed to print a given number of digits.  Clearly for approximations containing more than a million digits, it is not practical or useful actually to print the results of a computation!  In reality having this in an electronic format is much prefered anyway.


digits pages sheets reams  thickness 
(cm)
 thickness 
(m)
 thickness 
(km)
10,000  0.01   
100,000 20 10  0.1   
1,000,000 200 100  0.01  
10,000,000 2,000 1,000 10 0.1  
100,000,000 20,000 10,000 20 100  
1,000,000,000 200,000 100,000 200 1,000 10 0.01 
10,000,000,000 2,000,000 1,000,000 2,000 10,000 100 0.1 
100,000,000,000 20,000,000 10,000,000 20,000 100,000 1,000 
  1,000,000,000,000   200,000,000   100,000,000 200,000 1,000,000 10,000 10 
  10,000,000,000,000   2,000,000,000   1,000,000,000   2,000,000   10,000,000 100,000 100 


With 22,400,000,000,000 (22.4 trillion) digits calculated (as of 2016) it would take a stack of sheets of paper roughly 224 km (or about 139 miles) thick to print the entire approximation.

Another perspective:  it would take about 4.5 million reams of paper to print the 22.4 trillion digits. At $2.50 per ream the paper cost would be over $11 million!