# Ex.8.1 Q2 Comparing Quantities - NCERT Maths Class 8

## Question

Convert the following ratios to percentages

(i) \(3:4\)

(ii) \(2:3\)

## Text Solution

**What is known?**

Ratios

**What is unknown?**

Percentages of given ratios

**Reasoning:**

A ratio is a comparison of any two quantities by division. A percent is a special ratio that compares any quantity to \(100,\) with \(100\) representing one whole.

**Steps:**

(i) \(3:4\)

Given data: \(3:4\)

\[\begin{align}\frac{3}{{4}}&{ \times 100}\\&= 3 \times 25\\&= 75\%\end{align}\]

The answer is \(75\% \)

(ii) \(2:3\)

Given data: \(2:3\)

**Type 1: Decimal Form**

\[\begin{align}\frac{2}{3} &\times 100\\&= 2 \times 33.33\\&= 66.67\% \end{align}\]

The answer is \(66.67\% \) (Decimal form)

**Type 2: Fractions Form**

\[\begin{align}\frac{{{2 \times 100}}}{{3}}&= \frac{{{200}}}{{3}}\\& = 66\frac{{2}}{{3}}{\% }\end{align}\]

The answer is \(\begin{align}{66}\frac{{2}}{{3}}\% \end{align}\) (Mixed fraction form)