# Ex.1.3 Q1 Number System Solution - NCERT Maths Class 9

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## Question

Write the following in decimal form and say what kind of decimal expansion each has:

i) \begin{align}\frac{36}{100}\end{align}

ii) \begin{align}\frac{1}{11}\end{align}

iii)  \begin{align}4 \frac{1}{8}\end{align}

iv)\begin{align}\frac{3}{13}\end{align}

v) \begin{align}\frac{2}{11}\end{align}

vi) \begin{align}\frac{329}{400}\end{align}

Video Solution
Number Systems
Ex 1.3 | Question 1

## Text Solution

Steps:

(i) \begin{align}\frac{{36}}{{100}}=0.36\end{align}

Terminating decimal.

(ii) \begin{align}\frac{1}{11}\end{align}

The remainder $$1$$ keeps repeating. \begin{align}\frac{1}{{11}} = 0.0909\end{align} and can be written as

\begin{align}\frac{1}{{11}} = 0.\overline {09} \end{align}

Non-terminating recurring decimal.

(iii)  \begin{align}4 \frac{1}{8}=\frac{33}{8}\end{align}

\begin{align}4\frac{1}{8} = 4.125\end{align}

Terminating decimal ($$∵$$ The remainder is zero)

(iv) \begin{align}\frac{3}{13}=0.23076923\end{align}

$$\because$$ We find the block of numbers $$230769$$ keep repeating.

This is non-terminating recurring decimal and is written as:

\begin{align}\,\frac{3}{{13}} = 0.\overline {230769} \end{align}

(v) \begin{align}\frac{2}{{11}} = 0.1818\end{align}

Here we find the block of numbers $$18$$ keep repeating. Hence this is a non-terminating recurring decimal and is written as:

\begin{align}~\frac{2}{11}=0.\overline{18}\end{align}

(vi) \begin{align}\frac{{329}}{{400}} = \frac{{329}}{{4 \times 100}}\end{align}

\begin{align}{\frac{82.25}{100}} \\ {=0.8225}\end{align}

Terminating decimal (∵ The remainder is zero)

Video Solution
Number Systems
Ex 1.3 | Question 1

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