Question

Question: A lecture period (50 min) is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Using

,$\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}\mathbf{}\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{=}\left(\frac{actual-approximation}{actual}\right)\mathbf{\times }\mathbf{100}$

find the percentage difference from the approximation.

Short answer

Answer

1. Duration of 1 microcentury is .
2. The percentage difference in the actual and approximate duration of the microcentury is 9%.

Step-by-step solution

Given data

The lecture period of 50 min is close to a microcentury.

Understanding the duration of micro century

A time period of amillionthof acentury, equal to 52minutesand 35.7seconds

(a) Determination of the duration of micro century 

Calculate the duration of 1 microcentury in minutes as follows:

$$\begin{gathered} 1microcentuary={10}^{6}century\left(\frac{100y}{1century}\right)\left(\frac{365day}{1y}\right)\left(\frac{24hr}{1day}\right)\left(\frac{60min}{1hr}\right) \\ =52.6min \end{gathered}$$

Thus, the duration of 1 micro century in minutes is 52.6 min .

(b) Determination of the percentage difference

The percentage difference can be calculated as follows:

$$\begin{gathered} percentagedifference=\left(\frac{\mathrm{actual}-\mathrm{approximation}}{\mathrm{actual}}\right)\times 100 \\ =\left(\frac{52.6-50}{52.6}\right)\times 100 \\ =0.049\times 100 \\ =4.9\% \end{gathered}$$

Thus, the percentage difference is 4.9%.