The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies, 1 microcentury = $ {10^{ - 6}} \times 100 $ years. How many microcenturies did you sleep yesterday?

Hint We will use the relation between minutes, years and microcenturies to determine the duration of the practical period examination and the amount of sleeping time in microcenturies. We know that each year has 365 days in which each day has 24 hours. So using these values we need to convert the time and find the answer.

Complete step by step answer
We’ve been given the normal duration of I. Sc. Physics practical period in Indian colleges is 100 minutes. Since we’ve also been given the relation of the microcentury with years as $ {10^{ - 6}} \times 100 $ , let us first determine the duration of the practical examination in years.
Since we know that a year has 365 days which has 24 hours each and an hour has 60 minutes, let us first calculate the exam duration in days by dividing the exam duration by the number of minutes in one hour and the number of hours in one day.
 $ \Rightarrow t = \dfrac{{100}}{{60 \times 24}} $
 $ \Rightarrow t = 0.069\,{\text{days}} $
The duration of the exam in years can be calculated as,
 $ \Rightarrow t = 0.069/365 $
 $ \Rightarrow t = 0.000189\,{\text{years}} $
Since 1 microcentury = $ {10^{ - 6}} \times 100 = {10^{ - 4}} $ years, the duration of the exam in microcenturies is
 $ \Rightarrow t = \dfrac{{0.000189}}{{{{10}^{ - 4}}}} $
 $ \Rightarrow t = 1.89\,{\text{microcenturies}} $
Since an adult usually sleeps around 8 hours or ( $ 8 \times 60 $ ) minutes in a day, we can calculate the time in microcenturies in a similar manner as we did above and get the time in microcenturies as,
 $ \Rightarrow t = \dfrac{{8 \times 60}}{{24 \times 60 \times 365 \times {{10}^{ - 4}}}} $
 $ \Rightarrow t = 9.13\,{\text{microcenturies}} $ .

Note
Such questions require us to convert the units of time into other less known units like microcenturies carefully. However, for practical scenarios, small-time durations are always counted in hours or minutes or in most common cases as seconds and not in microcenturies.