Question

How do you write $13.8\mathrm{\%}$ as a decimal?

Answer 1

Hint: To convert a percent into a decimal, we will have to convert it into a fraction first. For converting it into a fraction, we will divide the percent by $100$. If the percent is a whole number, we will just simplify the fraction. But if the percent is not a whole number (as is the case here), we will multiply both the numerator and denominator with $1$ followed by as many zeroes as there are numbers after the decimal point in the percent. After converting it, we will turn the fraction obtained into an equivalent fraction which has $10$, $100$, $1000$ or $1$ followed by $0s$ as the denominator. Then, we will just write down the numerator, putting the decimal point at the correct place. The correct place is one space from the right-hand side for every zero in the denominator.

Complete step by step solution:
Given percent is $13.8\mathrm{\%}$.
Now, we will divide $13.8$ by $100$, such that
$\Rightarrow {\displaystyle \frac{13.8}{100}}$
Since $13.8$ is not a whole number, therefore we will multiply both the numerator and denominator with $10$ as there is only one digit after the decimal point. Therefore, the fraction becomes
$\Rightarrow {\displaystyle \frac{13.8\times 10}{100\times 10}}$
$\Rightarrow {\displaystyle \frac{138}{1000}}$
Since the fraction already has $1000$ in the denominator, we will just convert it into a decimal by writing down the numerator and putting the decimal point at the correct place. Here, the correct place will be $3$ spaces from the right-hand side of $138$, as there are $3$ zeroes in the denominator. Therefore we will get,
$\Rightarrow {\displaystyle \frac{138}{1000}}=0.138$

Hence, $13.8\mathrm{\%}$ can be written in decimal form as $0.138$.

Note:
$13.8\mathrm{\%}$ can be converted into a decimal by an alternate method also. After converting $13.8\mathrm{\%}$ into a fraction, we have got ${\displaystyle \frac{138}{1000}}$. After simplifying this fraction into its simplest form, we will get ${\displaystyle \frac{69}{500}}$. Now to convert ${\displaystyle \frac{69}{500}}$ into a decimal, we can perform the long division method.