Question

What is $16\dfrac{2}{3}\% $ as a fraction and 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. We are given a percentage in this question and we have to express it as a fraction and a decimal. So, we can do so by following the above steps.

Complete step by step answer:
The given question requires us to convert $16\dfrac{2}{3}\% $ into fraction and decimal. We have to first convert the percentage into fraction and then change it into decimal expansion.
First the given percentage is in the form of a mixed fraction. We convert the mixed fraction into an improper fraction. So, we get,
$16\dfrac{2}{3}\% = \dfrac{{3 \times 16 + 2}}{3}\% = \dfrac{{50}}{3}\% $
Now, we have to convert $\dfrac{{50}}{3}\% $ into a fraction and decimal.
On dividing $\dfrac{{50}}{3}\% $ by $100$, we get $\dfrac{{50}}{{300}}$.
Hence, $\dfrac{{50}}{3}\% $ in the fraction is $\dfrac{{50}}{{300}}$.

Now, we cancel the common factors in numerator and denominator to get the fraction in the simplest form .So, we get,
$ \Rightarrow \dfrac{{50}}{{300}} = \dfrac{1}{6}$
Hence, the percentage $16\dfrac{2}{3}\% $ can be represented as $\dfrac{1}{6}$ in fraction form.
Now, we have to change the fraction into the decimal expression.
So, $\dfrac{{50}}{{300}} = \dfrac{{16.67}}{{100}}$
Now, we know that 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,
$ \therefore \dfrac{{50}}{{300}} = 0.1667$

So, the percentage $16\dfrac{2}{3}\% $ can be represented as $0.1667$ in decimal form.

Note:We write percentage in 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.