Question

3. A lecture period (50 min) is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Calculate the percentage uncertainty (error) of that approximation. 5

Answer 1

(a) We know that
1 micro = 10^-6
1 century = 100 Years
1 years = 365 days
1 days = 24 hours
1 hour = 60 mins
Now
$1 microcentury = \left ( \frac{10^{-6}Century}{1} \right )\left ( \frac{100 Years}{1} \right )\left ( \frac{365 days}{1} \right )\left ( \frac{24 hours}{1 day} \right )\left ( \frac{60 mins}{1 hours} \right )$
1 micro-century = 52.56 mins
(b)
Now error in approximation
$Percentage Error = \left ( \frac{52.56 - 50}{52.56} \right )*100$
Percentage error = 4.87 %