Question

In high school, some students have been confused to believe that 22/7 is already the actual value of π or an acceptable approximation. Show that 355/113 is a better approximation in terms of absolute and relative errors.

Answer 1

Answer:

Since it has smaller absolute and relative errors, 355/113 is a better aproximation for $\pi$ than 22/7

Step-by-step explanation:

The formula for the absolute error is:

Absolute error = |Actual Value - Measured Value|

The formula for the relative error is:

Relative error = |Absolute error/Actual value|

I am going to consider the actual value of $\pi$ as 3.14159265359.

In the case of 22/7:

22/7 = 3.14285714286.

Absolute error = |3.14159265359 - 3.14285714286| = 0.00126448927

Relative error = 0.00126448927/3.14159265359 = 0.00040249943 = 0.04%

In the case of 355/113

355/113 = 3.14159292035

Absolute error = |3.14159265359 - 3.14159292035| = 0.00000026676

Relative error = 0.00000026676/3.14159265359 = 0.000000085 = 0.0000085%

Since it has smaller absolute and relative errors, 355/113 is a better aproximation for $\pi$ than 22/7