Question

How do you convert $2\dfrac{1}{5}$ into a decimal and a percent?

Answer 1

Hint: In this problem we need to convert the given fraction into the decimal and a percent. We can observe that the given fraction is a mixed fraction. So, we need to convert the given mixed fraction into the standard form of the fraction which is $\dfrac{a}{b}$. After that, we will consider the denominator and find a constant with which we need to multiply the denominator to convert the denominator to $100$. After converting the denominator to $100$, we will place the decimal value after the two digits from the right side. After getting the decimal value of the given fraction we will multiply the obtained decimal value with $100%$ and simplify the obtained equation to get the percentage value of the given fraction.

Complete Step by Step Procedure:
Given that, $2\dfrac{1}{5}$.
We can observe that the given fraction is the mixed fraction. Converting the mixed fraction into standard from
$\begin{align}
  & 2\dfrac{1}{5}=\dfrac{2\times 5+1}{5} \\
 & \Rightarrow 2\dfrac{1}{5}=\dfrac{11}{5} \\
\end{align}$
Now the standard form of the given mixed fraction $2\dfrac{1}{5}$ is $\dfrac{11}{5}$ .
In the above fraction, we can observe that the denominator is $5$. We know that we need to multiply the number $5$ with $20$ to get the denominator at $100$.
Multiplying both numerator and numerator with $20$. Then we will get
$\dfrac{11}{5}=\dfrac{11}{5}\times \dfrac{20}{20}$
Multiplying the numerator with numerator and denominator with the denominator then we will get
$\Rightarrow \dfrac{11}{5}=\dfrac{220}{100}$
Now we are going to place the decimal point after the two digits from the right side, then we will get
$\Rightarrow \dfrac{11}{5}=2.20$
Hence the decimal form of the given fraction $2\dfrac{1}{5}$ is $2.20$.
To convert the above decimal form into percentage we are going to multiple the above value with $100%$, then we will get
$\Rightarrow 2.20=2.20\times 100%$
Simplifying the above equation, we will get
$\Rightarrow 2.20=220%$.

Hence the percentage form of the given fraction $2\dfrac{1}{5}$ is $220%$.

Note:
In this problem, we have converted the denominator in the given fraction as $100$ to convert the given fraction into a decimal. You can also divide the numerator in the fraction with the given denominator.