Question

How do you convert $0.18$ into a fraction and percent?

Answer 1

Hint:In this problem we have converted expression into a fraction and percentage. First, we need to convert the given decimal value into a fraction. For this, we need to observe the given decimal value and we will divide the given decimal value with ${{10}^{n}}$ where $n$ is the number of digits that are there in the decimal after the decimal point. Now we will simplify the obtained equation to get the fraction form of the given decimal value. Up to this, the first part is completed. Now we need to convert the given decimal into a percentage. For this, we can directly use the given decimal value or we can use the fraction that has been obtained in the first part. To convert the decimal or fraction into percentage we need to multiply the value with $100\%$ to get the required result.

Complete step by step solution:
Given that, $0.18$
We can observe that the given decimal value has $2$ digits after the decimal point which are $1$, $8$. To convert the given decimal into a fraction we need to divide the above value with ${{10}^{n}}={{10}^{2}}$. Then we will have
$\Rightarrow$ $0.18=\dfrac{18}{{{10}^{2}}}$
We know that ${{10}^{2}}=100$. Substituting this value in the above equation, then we will get.
$\Rightarrow$ $0.18=\dfrac{18}{100}$
Hence the fraction form of the decimal $0.18$ is $\dfrac{18}{100}$.
To convert the given decimal value into a percentage, we are going to multiply $100\%$ to the above-obtained fraction, then we will get
$\Rightarrow$ $0.18=\dfrac{18}{100}\times 100\%$
Canceling the $100$ which is in both numerator and denominator, then we will get
$\Rightarrow$ $0.18=18\%$.
Hence the percentage form of the decimal $0.18$ is $18\%$.

Note: In this problem, we have written the fraction form of the decimal value $0.18$ as $\dfrac{18}{100}$ for an easy calculation in further steps i.e., calculation of percentage form. We can simplify the fraction $\dfrac{18}{100}$ by writing the factors of both numerator and denominator and canceling the common factors in both numerator and denominator, then we will get our simplified fraction form.