Question

What is $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour?

Answer 1

Hint: In this problem we need to find the $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour. For this first we will calculate the $\dfrac{1}{60}$ of an hour by multiplying both the values. That means we will multiply $\dfrac{1}{60}$ with $1$ hour. Here we will use the relation $1\text{ Hour}=60\text{ Minutes}$. After substituting this relation, we will simplify the obtained equation by using basic mathematical operations. After having the value of $\dfrac{1}{60}$ of an hour again we will multiply it with $\dfrac{1}{60}$ to get the value of $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour which is our required value. Here we will use the substitution $1\text{ Minute}=60\text{ Seconds}$, after substituting this value we will simplify the equation by using basic mathematical operations to get the required result.

Complete step by step solution:
Given $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour.
Considering the value $\dfrac{1}{60}$ of an hour. The value $\dfrac{1}{60}$ of an hour is calculated by multiplying $\dfrac{1}{60}$ with $1$ hour, then we will get
$\dfrac{1}{60}\text{ of an hour}=\dfrac{1}{60}\times 1\text{ hour}$
Substituting the relation $1\text{ Hour}=60\text{ Minutes}$ in the above equation, then we will have
$\dfrac{1}{60}\text{ of an hour}=\dfrac{1}{60}\times 60\text{ Minutes}$
Cancelling the term $60$ which is in both numerator and denominator in the above equation, then we will get
$\dfrac{1}{60}\ \text{of an hour}=1\text{ Minute}$
Now the value of $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour is calculated by again multiplying $\dfrac{1}{60}$ to the above calculated value, then we will have
$\dfrac{1}{60}\text{ of }\dfrac{1}{60}\ \text{of an hour}=\dfrac{1}{60}\times 1\text{ Minute}$
Substituting the relation $1\text{ Minute}=60\text{ Seconds}$ in the above equation, then we will get
$\dfrac{1}{60}\text{ of }\dfrac{1}{60}\text{ of an hour}=\dfrac{1}{60}\times 60\,\text{Seconds}$
Cancelling the term $60$ which is in both numerator and denominator in the above equation, then we will have
$\dfrac{1}{60}\text{ of }\dfrac{1}{60}\text{ of an hour}=1\,\text{Second}$.

Hence the value of $\dfrac{1}{60}$ of $\dfrac{1}{60}$ of an hour is $1$ second.

Note: For this problem we can also use another method in which we will directly multiply both the $\dfrac{1}{60}$’s to one hour and use the relation $1\text{ Hour}=3600\ \text{Seconds}$. After that we will use some basic mathematical operations to get the required result.