Question

What percent is 1 min 48 seconds of 1 hour?

Answer 1

Hint: We need to find what is 1 min 48 seconds as the percent of 1 hour. Firstly, we start to solve the problem by expressing 1 min 48 seconds and 1 hour in the form of seconds. Then, we divide the value of 1 min 48 seconds in seconds by the value of 1 hour in seconds. Lastly, we multiply the result of division by 100 to get the desired result.

Complete step-by-step solution:
A percentage is a value expressed as a fraction of a hundred or $\dfrac{1}{100}$ . It is denoted by the symbol ’$\%\;$’. The value expressed as a percentage does not have any dimension or unit of measurement.
For Example:
$\Rightarrow 2\%,3\%$
According to the question,
We are required to express 1 min 48 seconds in the form of seconds.
The value of 1 min 48 seconds can be written as follows,
$\Rightarrow 1\min \text{48seconds}=1\min +48\text{seconds}$
We know that one minute has 60 seconds. Following the same, we get,
$\Rightarrow 1\min \text{48seconds}=60\text{seconds}+48\text{seconds}$
Simplifying the above equation, we get,
$\therefore 1\min \text{48seconds}=108\text{seconds}$
We know that one hour has 60 minutes. Following the same, we get,
$\Rightarrow 1\text{hour}=60\text{minutes}$
We know that one minute has 60 seconds. Following the same, we get,
$\Rightarrow 1\text{hour}=60\times 60 \text{seconds}$
Simplifying the above equation, we get,
$\therefore 1\text{hour}=3600 \text{seconds}$
Now, we need to divide the value of 1 min 48 seconds in seconds by the value of 1 hour in seconds.
Dividing the value of 1 min 48 seconds in seconds by the value of 1 hour in seconds, we get,
$\Rightarrow \dfrac{108}{3600}$
We need to multiply the above expression by 100 to get the value in terms of percentage.
Multiplying the above expression by 100, we get,
$\Rightarrow \dfrac{108}{3600}\times 100\%$
Canceling the common factors, we get,
$\Rightarrow 3\%$
$\therefore$ $3\%\;$ of 1 hour is $1\min \text{48seconds}$

Note: The given question can be solved alternatively as follows,
A particular quantity can be expressed as the percentage of the other by simply multiplying the fraction of the quantity by $100\%\;$
In our case,
Fraction $=\dfrac{1\min \text{ 48seconds}}{1\text{hour}}$
Converting the numerator and the denominator of the fraction into seconds, we get,
$Fraction=\dfrac{\text{108}}{3600}$
$\Rightarrow fraction\times 100\%$
Substituting the value of the fraction in the above expression, we get,
$\Rightarrow \dfrac{108}{3600}\times 100\%$
$\Rightarrow 3\%$