Question

How do you write the fraction $\dfrac{8}{9}$ as a percent$?$

Answer 1

Hint: Given fraction in question is proper fraction because according to the definition of a proper fraction
The denominator is always greater than the numerator.
The fraction $\left( \dfrac{a}{b} \right)$ has two-part on the top of the fraction $a$ is called the numerator and the bottom of the fraction $b$ is called the denominator.
To change the fraction into percent multiply it by $100$ and divide by $100$. When we divide that number to change or convert by $100$ it represents the symbol:$%$.
For example, the fraction is $\dfrac{a}{b}$, and to convert it to percent we will multiply it by $100$ and divide it by $100$.
$\Rightarrow \dfrac{a}{b}\times \dfrac{100}{100}$
$\Rightarrow \dfrac{100a}{b}\times \dfrac{1}{100}$
$\Rightarrow \dfrac{100a}{b}%$
The percent is ${{\left( \dfrac{1}{100} \right)}^{th}}$ part of any whole number or fraction or decimal number.

Complete step by step solution:
The given fraction in question is $\dfrac{8}{9}$.
To write $\dfrac{8}{9}$ in percent we need to change it into the decimal value of this fraction.
The decimal value of the fraction $\dfrac{8}{9}$ is
$\Rightarrow \dfrac{8}{9}=0.88888888...$
We can write it as $\dfrac{8}{9}=0.\overline{8}$.
To write this decimal value $0.88888$ in percent then multiply it by $100$ and divide by $100$
$\Rightarrow (0.88888...)\times \dfrac{100}{100}$
$\Rightarrow (88.8888...)\times \dfrac{1}{100}$
The fraction with the denominator $100$ is percent.
$\Rightarrow 88.8888...%$
We can rewrite it as
$\Rightarrow 88.9%$

Thus the percent value of the fraction $\dfrac{8}{9}$ is $88.9%$.

Note: To change the fraction into the percentage divide and multiply that fraction by $100$.
Like $\dfrac{a}{b}\times \dfrac{100}{100}$ where the denominator $100$ is represented $%$.