Question

Convert the following percentage into decimal fraction.
(i) \[40\% \]
(ii) \[25\% \]

Answer 1

Hint: Here we use the concept of percentage that percentage of any number can be written in fraction form where the numerator is the number itself and denominator is 100. After writing the percentage in fraction form, we make the fraction in simplest form by cancelling out all possible factors from numerator and denominator such that we have the numbers 10 or 100 in the denominator.
* \[x\% = \dfrac{x}{{100}}\]
* Percentage is a part of the whole. It is a way to represent the selected data in terms of percentage from the whole data.
* Decimal fraction is a fraction that has a denominator as 10, 100, 1000 etc.

Complete step-by-step answer:
We know that percentage can be converted into fraction by writing it in the form \[x\% = \dfrac{x}{{100}}\].
(i) \[40\% \]
Since, we have to convert \[40\% \] into decimal fractions.
Substitute the value of x as 40 in the formula \[x\% = \dfrac{x}{{100}}\].
\[ \Rightarrow 40\% = \dfrac{{40}}{{100}}\]
Now we can write the numerator and denominator in terms of their factors
\[ \Rightarrow 40\% = \dfrac{{4 \times 10}}{{10 \times 10}}\]
Cancel 10 from numerator and denominator.
\[ \Rightarrow 40\% = \dfrac{4}{{10}}\]
Therefore, the decimal fraction of \[40\% \] is \[\dfrac{4}{{10}}\].
(ii) \[25\% \]
Since, we have to convert \[25\% \] into decimal fractions.
Substitute the value of x as 40 in the formula \[x\% = \dfrac{x}{{100}}\].
\[ \Rightarrow 25\% = \dfrac{{25}}{{100}}\]
Now we can write the numerator and denominator in terms of their factors
\[ \Rightarrow 25\% = \dfrac{{5 \times 5}}{{10 \times 10}}\]
Since, we can see that if we cancel any factor from numerator and denominator, the denominator will not be in the form of 10 or 100, so we cancel nothing from numerator and denominator.
\[ \Rightarrow 25\% = \dfrac{{25}}{{100}}\]
Therefore, the decimal fraction of \[25\% \] is \[\dfrac{{25}}{{100}}\].

Note: Students many times make mistake of converting the fraction into decimal form by dividing the numerator by denominator which is wrong because here we have to give our answer in terms of decimal fraction which has denominator as \[{10^n}\] for any value of n.