Question

What is $25\% $ of $25\% $ equal to
A. $6.25$
B. $0.625$
C. $0.0625$
D. $0.00625$

Answer 1

Hint:In the above question we will first convert both the percentage into simpler form i.e. simpler form and then we multiply them. We know that a percentage is a number or ratio expressed as a fraction of $100$ . It is denoted using the percentage sign i.e.
$\% $. It does not have any other dimension. The term “of” means to multiply in the above question.

Complete step by step answer:
We should know that percentage is a part of the whole. It is a way to represent the selected data in terms of percentage from the whole data. A whole is represented by $100\% $.According to the question we have two percentage terms. First term is $25\% $.
We can break the percentage by dividing the fraction by hundred:
$25 \times \dfrac{1}{{100}} = \dfrac{{25}}{{100}}$.
Now the decimal form of the first percentage term is
 $\dfrac{{25}}{{100}} = 0.25$

Now we move to the second term which is $25\% $. Similarly as above we can break the percentage by dividing the fraction by hundred:
$25 \times \dfrac{1}{{100}} = \dfrac{{25}}{{100}}$
Since the terms are same, so the decimal form of the second percentage term is also the same: $\dfrac{{25}}{{100}} = 0.25$
Now we can put the values back in the expression:
$0.25$ of $0.25$
We can write of as multiply and it gives,
$0.25 \times 0.25 = 0.0625$

Hence the correct option is C.

Note: We should know that the formula of percentage is: $\dfrac{{Value}}{{Total\,value}} \times 100\% $. We can use this formula to calculate the total value when the value and the percentage is given. We should note that we have multiplied the decimal numbers in the above solution. We can simplify the expression as,
$0.25 \times 0.25 = \dfrac{{25}}{{100}} \times \dfrac{{25}}{{100}}$
We can multiply the numerator and the denominator of the fraction and it gives:
$\dfrac{{625}}{{1000}}$
Now we know that this is a decimal number. The denominator can be written as $10000 = {10^4}$. So we can see that the denominator has the power $4$.So we place the decimal point before the four digits from the left in the numerator.Hence we have
$\dfrac{{625}}{{{{10}^4}}} = 0.0625$