Question

What is the percentage error in using $\frac{22}{7}$ as an approximation for $\pi$?
(Give your answer to the nearest $0.01$)

• A. $0.02\%$
• B. $0.03\%$
• C. $0.04\%$
• D. None of these

Answer 1

Answer: (C)

$0.04\%$

$\Rightarrow$ Here, Approximate value of $\pi$ = $\frac{22}{7}=3.142857$

$\Rightarrow$ Exact value of $\pi$ is $3.141592$

$\Rightarrow$ $\%Error=\frac{|Approximatevalue-Exactvalue|}{|Exactvalue|}\times 100$

$\Rightarrow$ $\%Error=\frac{|3.142857-3.141592|}{|3.141592|}\times 100$

$\Rightarrow$ $\%Error=0.04\%$