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 ${\displaystyle \frac{1}{100}}$ . It is denoted by the symbol ’$\mathrm{\%}$’. The value expressed as a percentage does not have any dimension or unit of measurement.
For Example:
$\Rightarrow 2\mathrm{\%},3\mathrm{\%}$
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,
$\Rightarrow 1min\text{48seconds}=1min+48\text{seconds}$
We know that one minute has 60 seconds. Following the same, we get,
$\Rightarrow 1min\text{48seconds}=60\text{seconds}+48\text{seconds}$
Simplifying the above equation, we get,
$\therefore 1min\text{48seconds}=108\text{seconds}$
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,
$\Rightarrow {\displaystyle \frac{108}{3600}}$
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,
$\Rightarrow {\displaystyle \frac{108}{3600}}\times 100\mathrm{\%}$
Canceling the common factors, we get,
$\Rightarrow 3\mathrm{\%}$
$\therefore$ $3\mathrm{\%}$ of 1 hour is $1min\text{48seconds}$

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 $100\mathrm{\%}$
In our case,
Fraction $={\displaystyle \frac{1min\text{ 48seconds}}{1\text{hour}}}$
Converting the numerator and the denominator of the fraction into seconds, we get,
$Fraction={\displaystyle \frac{\text{108}}{3600}}$
$\Rightarrow fraction\times 100\mathrm{\%}$
Substituting the value of the fraction in the above expression, we get,
$\Rightarrow {\displaystyle \frac{108}{3600}}\times 100\mathrm{\%}$
$\Rightarrow 3\mathrm{\%}$