Question

How do you express $30\% $ of $\dfrac{4}{3}$ as a decimal?

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. Next, multiply the decimal fraction of $30\% $ with $\dfrac{4}{3}$. Cancel 3 from numerator and denominator and put decimal before one digit of numerator.
(i). $x\% = \dfrac{x}{{100}}$
(ii). Percentage is a part of the whole. It is a way to represent the selected data in terms of (iii). percentage from the whole data.
Decimal fraction is a fraction that has a denominator as 10, 100, 1000 etc.

Complete step-by-step solution:
We know that percentage can be converted into fraction by writing it in the form $x\% = \dfrac{x}{{100}}$.
Since, we have to convert $30\% $ into fractions.
Substitute the value of $x$ as 30 in the formula $x\% = \dfrac{x}{{100}}$.
$ \Rightarrow 30\% = \dfrac{{30}}{{100}}$
Now we can write the numerator and denominator in terms of their factors
$ \Rightarrow 30\% = \dfrac{{3 \times 10}}{{10 \times 10}}$
Cancel 10 from numerator and denominator.
$ \Rightarrow 30\% = \dfrac{3}{{10}}$
Therefore, the decimal fraction of $30\% $ is $\dfrac{3}{{10}}$.
Now, multiply the decimal fraction of $30\% $ with $\dfrac{4}{3}$.
$30\% {\text{ of }}\dfrac{4}{3} = \dfrac{3}{{10}} \times \dfrac{4}{3}$
Cancel 3 from numerator and denominator.
$ \Rightarrow 30\% {\text{ of }}\dfrac{4}{3} = \dfrac{4}{{10}}$
Put decimal before one digit of the numerator.
$\therefore 30\% {\text{ of }}\dfrac{4}{3} = 0.4$
Therefore, $30\% $ of $\dfrac{4}{3}$ in decimal form is $0.4$.

Note: Students many times make the mistake of converting the fraction into decimal fraction in terms of decimal fraction which has denominator as $10n$ for any value of $n$ which is wrong because here we have to give our answer in terms of decimal.