I calculated the absolute error of that(where x' is the machine number)

x' = **3.1415926**45

x= **3.1415926**53 (actual value)

Code:

|ε| = |x - x'| = 0.000000008 = 0.08 * 10^(-7) < 0.5*10^(-7)

which tell us that the machine value is going to be accurate at 7 decimal digits at the most.Here it is exact 7 digits.

Then i calculated the absolute relative error

Code:

|ρ| = |ε| / x = 0,025464790899483937645941521750815 * 10^(-7) = 0,025464790899483937645941521750815 * 10^(-9) < 5 * 10^(-9)

which says that at the most nine significant digits are going to be accurate.Here 8 digits are accurate.

However i think that this accuracy is satisfactory for a school exercise,so the series i gave before i think is enough