Question

Convert the following ratio into percentage: $\dfrac{22}{30}$?

Answer 1

Hint: In this question, we have to convert the given ratio into percentage. To convert into percent, the ratio will be multiplied by 100%. Before that, this ratio has to be reduced in the simplest form. The ratio is already given in the form of a fraction.

Complete step by step solution:
Now, let’s begin to solve the question.
Ratio is the value which can be written with the symbol ‘:’ or can be denoted in the form of a fraction. For example: if we are given 4:3, it can also be expressed as $\dfrac{4}{3}$. Here also in the given question, $\dfrac{22}{30}$
Is not only the ratio but can also be called as a fraction. We have to convert the given ratio in to percentage. For that, we have to multiply the given ratio with $\dfrac{100}{100}$. 100 in the denominator is used to express a percentage with a % symbol. That means we have to multiply the given ratio with 100%. The result we obtain will also be expressed with this symbol.
$\Rightarrow \dfrac{22}{30}\times 100\%$
Now, the next step is to reduce the terms and obtain the value in the simplest form. First cancel the zero from numerator and denominator:
$\Rightarrow \dfrac{22}{3}\times 10\%$
As we can see, the terms will not get reduced anymore, so we will multiply and divide with 3:
$\Rightarrow \dfrac{220\%}{3}$
$3\overset{73.3}{\overline{\left){\begin{align}
  & 220 \\
 & 21 \\
 & \overline{010} \\
 & \text{ }9 \\
 & \overline{\text{ }10} \\
 & \text{ }9 \\
 & \overline{\text{ }1}\text{ } \\
\end{align}}\right.}}$
So the answer will be 73.3%.

Note: We used long division above for dividing the terms. If we are expressing any number in the form of a percentage, then the% symbol has to be written with it otherwise you will not get any marks. We haven’t reduced $\dfrac{22}{30}$ above before multiplying it with 100% because it would have increased the calculations. To make calculations easy, the above steps are performed.