91Ó°ÊÓ

The absolute error refers to the difference in the observed value and the true value of a quantity.

The maximum absolute error in measurement of 1 year, $\mathrm{Δ}t=Â\pm 8\mathrm{s}$.

The formula for percentage error is written as

$\mathrm{percentage}\mathrm{error}=\frac{\mathrm{absolute}\mathrm{error}}{\mathrm{expected}\mathrm{value}}×100$.

After 1 year, the expected value of measurement will be

$\begin{array}{c}\mathrm{expected}\mathrm{value}=1×365×24×60×60\\ =3,15,36,000\mathrm{s}\end{array}$

Substituting the values in the formula for percentage error,

$\begin{array}{c}\mathrm{percentage}\mathrm{error}=\frac{\mathrm{Δ}t}{3,15,36,000}×100\\ =\frac{Â\pm 8}{3,15,36,000\mathrm{s}}×100\\ =2.54×{10}^{-5}\%\end{array}$

Percentage accuracy can be written in terms of percentage error as

Percentage accuracy = 100 – percentage error.

Substituting the values in the above equation,

Percentage accuracy = 99.9999746%.

Thus, the percentage accuracy is 99.9999746%.