Question

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

Answer 1

Hint: From the given question we have to write the decimal of $\dfrac{2}{5}$ and its percentage. To find the decimal of $\dfrac{2}{5}$. We know that if a fraction is written with a denominator which is a power of 10 then it can be written as a decimal. We also know that a fraction with a denominator of 100 is immediately the same as a percentage and we can represent percentage using the first 2 decimal places after the decimal point. The way to make the denominator ten is to multiply both the numerator and denominator by $ \dfrac{10}{\text{denominator}}$. By this we can find the decimal of $\dfrac{2}{5}$. Then by multiplying numerator and denominator with 10 then we will get a percentage.

Complete step-by-step solution:
From the question given we have to find the decimal and percentage of
$\Rightarrow \dfrac{2}{5}$
First, we will find the decimal.
As we know that to write the decimal, we have to make the denominator $10$.
The easiest way to write this as a decimal is to multiply it until the denominator is $10$. As decimals are written in a ten’s system (with a tenth, hundredths, thousandths, etc. place), fractions with a denominator of $10$ can easily be written as decimals.
The way to make the denominator ten is to multiply both the numerator and denominator by
$\Rightarrow \dfrac{10}{\text{denominator}}$
 Here in this case, we have to multiply both the numerator and denominator by
 $\Rightarrow \dfrac{10}{5}$
By multiplying we will get,
$\Rightarrow \dfrac{2}{5}\left( \dfrac{\dfrac{10}{5}}{\dfrac{10}{5}} \right)$
 $\Rightarrow \dfrac{2}{5}\left( \dfrac{2}{2} \right)$
 $\Rightarrow \dfrac{4}{10}$
$\Rightarrow 0.4$
 Therefore, the decimal of $\dfrac{2}{5}$ is $0.4$.
Now for the percentage we have to make the denominator $100$
By multiplying the numerator and denominator with $10$ we will get the denominator as $100$ then we will get the percent,
$\Rightarrow \dfrac{4}{10}\left( \dfrac{10}{10} \right)$
$\Rightarrow \dfrac{40}{100}$
$\Rightarrow 40\%$
Therefore, the percentage is $40$.

Note: Students should know the easiest method to solve or convert the given number into the decimal. Students can also solve this by using long division. Students should make the denominator as $\left( 10,100,100.. \right)$ by this they can write the decimal forms very easily. Student can find the percentage by multiplying the number with $100\%$, for example,
$\Rightarrow \dfrac{2}{5}\times 100\%$
$\Rightarrow 40\%$
Here $100$ will be used in the multiplication that is in the calculation and $\%$ will be the sign in the answer.