# Ex.8.2 Q6 Compairing Quantities - NCERT Maths Class 7

## Question

Convert given per cents to decimal fractions and also to fractions in simplest forms:

(a) \(25\%\)

(b) \( 150\%\)

(c) \(20\% \)

(d) \( 5\%\)

## Text Solution

**What is Known?**

Percentages.

**What is Unknown?**

Decimal fractions and fractions in simplest forms of given percentages.

**Reasoning:**

To convert given percentage into decimal fractions, divide it by \(100\) and to convert the fraction to its simplest form, divide both the numerator and denominator by the common factor. Repeat this process until there are no more common factors. The fraction thus obtained is the simplest form of the fraction.

**Steps:**

(a) \(25\%\)

So, decimal fraction will be

\[\begin{align}& = \frac{{25}}{{100}}\\& = 0.25\end{align}\]

& Simplest form of fraction will be

\[\begin{align}\frac{{25}}{{100}} & = \frac{5}{{20}}\\ & = \frac{1}{4}\end{align}\]

(b) \(150\%\)

So, decimal fraction will be

\[\begin{align}& = \frac{{150}}{{100}}\\&={1.50}\end{align}\]

& Simplest form of fraction will be

\[\begin{align}\frac{{150}}{{100}} & = \frac{{30}}{{20}}\\& = \frac{3}{2}\end{align}\]

(c) \(20\%\)

So decimal fraction will be

\[\begin{align}& = \frac{{20}}{{100}}\\& = 0.20\end{align}\]

& Simplest form of fraction will be

\[\begin{align}\frac{{20}}{{100}} & = \frac{2}{{10}}\\ & = \frac{1}{5}\end{align}\]

(d) \(5\%\)

So decimal fraction will be

\[\begin{align}& = \frac{5}{{100}}\\& = 0.05\%\end{align}\]

& Simplest form of fraction will be

\[\begin{align}\frac{5}{{100}} & = \frac{1}{{20}}\end{align}\]

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