Question

How do you find $5\%$ of $32.68\;$ ?

Answer 1

Hint:Firstly, write the expression in percentage form i.e., expand the percentage symbol. Write it in terms of $\dfrac{1}{{100}}$ . Now multiply it with the decimal. We are multiplying because they said $5\%$ “of” which symbolizes multiplication to that constant. Now evaluate the expression to get the answer. Cross-check by substituting and getting the question back.

Complete step by step answer:The given expression which is needed to be solved is $5\%$ of $32.68\;$
Now write the percentage symbol into fraction form
We write the percentage symbol as $\dfrac{1}{{100}}$.
On rewriting the expression, we get,
$\Rightarrow 5 \times \dfrac{1}{{100}}$ of $32.68\;$
Now we symbolize “of” as a multiplication operator.
$\Rightarrow 5 \times \dfrac{1}{{100}} \times 32.68$
Now start evaluating the expression.
$\Rightarrow \dfrac{1}{{20}} \times 32.68$
Now convert the decimal into a fraction.
$\Rightarrow \dfrac{1}{{20}} \times \dfrac{{3268}}{{100}}$
On further simplification we get,
$\Rightarrow \dfrac{{1634}}{{1000}}$
We now convert this back into decimal form.
$\Rightarrow 1.634$
Units can be ignored while evaluation but must be written while writing the end solution.
Here the units are dollars.
$\therefore 5\%$ of $32.68\;$ is $1.634\;$
We can cross-check our answer by placing it back into the expression.
We shall find the percent given in the question from our answer.
 $\Rightarrow x \times 32.68 = 1.634$
$\Rightarrow x = \dfrac{{1.634}}{{32.68}}$
Write decimals into fractions.
$\Rightarrow x = \dfrac{{1634 \times \dfrac{1}{{1000}}}}{{3268 \times \dfrac{1}{{100}}}}$
Now simplify further to get,
$\Rightarrow x = \dfrac{{1634 \times \dfrac{1}{{10}}}}{{3268}}$
We get,
$\Rightarrow x = 0.05$
Now to write this into percent form multiply it with a hundred
$\Rightarrow x = 0.05 \times 100 = 5\%$
Hence proved that our answer is correct.

Note:
Since the word percentage means how much of one quantity can be expressed in between $1 - 100$ , Whenever there is a percent symbol which is denoted by $\%$ symbol, convert it into the fraction, $\dfrac{1}{{100}}$ and to convert a fraction into percentage always multiply it with $100\;$ . Cross-check answers by placing the solution in the question and then finding any other random variable.