15 - University Physics with Modern Physics

Question

A useful and easy-to-remember approximate value for the number of seconds in a year is 𝛑 × 10⁷. Determine the percent error in this approximate value. (There are 365.24 days in one year.)

 

Step-by-Step Solution

Answer

The percent error in the approximate value is 0.44%.

Definition

Given data:

The approximate values .

 $e_{approx}=\mathrm{\pi }\times {10}^7$

The percent error is the difference between the actual value and estimated value in a comparative manner with actual value as a percentage.

 

Explanation

The value of 365.24 days in second will be,

$$\begin{gathered} e_{actual}=365.24 days \\ {e}_{actual}=365.24 days\times \frac{86400 s}{1 day} \\ {e}_{actual}=31556736 s \end{gathered}$$

 

The percent error can be calculated as,

$$\begin{gathered} \% error=\frac{e_{actual}-e_{approx}}{e_{actual}}\times 100\% \\ =\frac{31556736-\mathrm{\pi }\times {10}^7}{31556736}\times 100\% \\ =0.44\% \end{gathered}$$

 

Thus, the percent error in the approximate value is 0.44%.