Question

A convenient substitution for the number of seconds in a year is pi time 10^7. To within what percentage error is this correct?

Answer 1

Answer:

0.38%

Explanation:

Seconds in a year(actual) = 365*24*60*60 = 3.1536 * 10^7

Seconds in a year(Estimated)=3.1416*10^7 which is nothing but pi*10^7

now percentage error = relative error * 100

     percentage error = $=\frac{3.1536-3.1416}{3.1536} *100\\=0.0038*100\\=0.38percentage$

Hence, the approximate substitution of pi for number seconds in a year has a percentage error of 0.38%