Question

What is $32\% $ as a decimal?

Answer 1

Hint: We use the concept of the percentage to find the proportion of the amount of a substance to a larger sum of substance. The percentage is represented by the symbol "\[\% \]". In mathematics, when a number or ratio is expressed as a fraction of \[100\], we get the percentage. In everyday life, the percentage is most important in financial aspects. By dividing the given percentage by \[100\], the percentage is converted into fraction form or decimal form, like $1\% $ in fraction form is $\left( {\dfrac{1}{{100}}} \right)$ and in decimal form is \[0.01\].

Complete step by step solution:
The given question requires us to convert $32\% $ into fractions and decimals. We have to first convert the percentage into fractions and then change it into decimal expansion.
So, we have, $32\% $
On dividing $32\% $ by $100$, we get $\dfrac{{32}}{{100}}$.
Hence, $\dfrac{{32}}{{100}}$ is the corresponding fraction of $32\% $.
Now, we can cancel the common factors in numerator and denominator so that the resulting fraction is in simplified form. But that would make the division and representation of the percentage in decimal form difficult.
We know that division by a power of ten is easier. For dividing any number by a power of ten, we just need to place a decimal point to the left of the same number of decimal places as the power of ten.
So, division of any decimal number by $100$ can be done by placing a decimal point two places to the left of the original place. Hence, we get,
$ \Rightarrow \dfrac{{32}}{{100}} = 0.32$
Therefore, the percentage $32\% $ can be represented as $0.32$ in decimal form.

Note:
We write the percentage in the statement form as: “x percent of some amount”. A Fraction is divided into two parts by a horizontal line. The part above the line is called the numerator and the part below the line is called the denominator. We must know to convert a mixed fraction into an improper fraction to tackle the given problem. We must take care of the calculations while converting the percentage into numerator and denominator to be sure of the final answer.