Question

What percentage of a day is \[6\text{hours}\] and \[45\text{minutes}\]?
1. \[7.218\% \]
2. \[8.3\% \]
3. \[28.125\% \]
4. None of these

Answer 1

Hint: In mathematics, a percentage is a number or ratio that can be expressed as a fraction of \[100\]. If we have to calculate percent of a number, divide the number by whole and multiply by \[100\]. Hence, the percentage means, a part per hundred. The word percent means per \[100\]. It is represented by the symbol “%”.

Complete step-by-step solution:
The percentage means, a part per hundred. The percentages have no dimension. Hence it is called a dimensionless number. Percentages can also be represented in decimal form or fraction form. It can also be said that a number or rate that is expressed as a certain number of parts of something divided into 100 parts or it can be said as a part of the whole.
To determine the percentage, we have to divide the value by the total value and then multiply the resultant to\[100\].
Percentage formula \[ = \dfrac{\text{value}}{\text{total value}} \times 100\]
To calculate the percentage of a number, we need to use a different formula such as:
\[P\% \times number = X\]
Where X is the required percentage.
If we remove the % sign, then we need to express the above formulas as:
\[\dfrac{P}{{100}} \times number = X\]
We know that a day has \[24hours\].
Now \[6hours\] and \[45\text{minutes}\]\[ = 6\dfrac{{45}}{{60}} = 6\dfrac{3}{4} = \dfrac{{27}}{4}hours\]
So % of a day\[ = \dfrac{{27}}{{4*24}} \times 100 = 28.125\% \]
Therefore option (3) is the correct answer.

Note: Percentages have no dimension. Hence it is called a dimensionless number. Percentages can also be represented in decimal or fraction form. To determine the percentage, we have to divide the value by the total value and then multiply the resultant to \[100\].