Computers are a very powerful tool. For example, the following Basic program illustrates their ability to represent and print extremely small numbers.

10 FOR k=0 TO 100
20 LET epsilon 2^(-k)
30 PRINT "k=", k, "epsilon", epsilon
40 NEXT k
50 END

But we must not over estimate their power. Edit the above program by replacing lone 20 with the one below and inserting line 356 between lines 30 and 40 and lines 44 and 45 between lines 40 and 50. Notice that as 2^(-k) becomes extremely small when executing the operation(1+2^(-k))-1 the computer approximates 2^(-k) by zero.

20 LET epsilon = (1+2^(-k))-1
35 IF epsilon = 0 THEN 44
44 LET e =k
45PRINT "e is", e, "Machine Epsilon is", 2^(-(e-1))

The number 2^-(e-1) is said to be the Machine Epsilon number and converting 2^-(e-1) to decimal representation gives the number of decimal digits your computer is accurate to.