Question

What percentage of a day is one hour and $ 45 $ minutes?
A) $ 7.218\% $
B) $ 8.3\% $
C) $ 7.291\% $
D) None of these

Answer 1

Hint: Percentage is the number or ratio expressed as a fraction of hundred. Here we will take the standard relation of hour to minute and total hours in a day and will simplify for the resultant required value.

Complete step by step solution:
We know that,
In one day there are $ 24 $ hours.
One hour is $ = 60 $ minutes
Now, we are given that to find the percentage in a day for one hour and $ 45 $ minutes.
Therefore, one hour and $ 45 $ minutes $ = 60 + 45 = 105 $ minutes.
One day $ = 24 $ hours $ = 24 \times 60 = 1440 $ minutes
Now, frame the given data to get the required percentage –
 $ = \dfrac{{105}}{{1440}} \times 100 $
Simplify the above expression –
 $ = 7.291\% $
Hence, one hour $ 45 $ minutes is $ 7.291\% $ of a day.

Therefore, option C is the correct answer.

Additional Information: To convert decimal into fraction, place the decimal number over its place value. For example, for $ 0.2 $ the two is in the tenths place so that we place $ 2 $ over $ 10 $ to create the equivalent fraction i.e. $ \dfrac{2}{{10}} $ and similarly if there is two digits after decimal point, for $ 0.25 $ the $ 25 $ is in the hundredths place so that we place $ 25 $ over $ 100 $ to create the equivalent fraction i.e. $ \dfrac{{25}}{{100}} $ .

Note: Be careful while simplifying equations and always remember when its percentage is with respect to hundred. Convert the decimal point in the form of fraction. Always remember that percentage is always based off $ 100\% $ so the decimals up to the hundredths place will always be integers and the numbers after the hundredths place will be after the decimal and the tens place in the percentage will always be in the tenths place in the decimal form as well.