Ex.8.1 Q2 Comparing Quantities - NCERT Maths Class 8

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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)

  
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