Ex.1.3 Q9 Number System Solution - NCERT Maths Class 9

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Question

Classify the following numbers as rational or irrational:

(i) \(\begin{align}\sqrt{23}\end{align}\)

(ii) \(\begin{align} \sqrt{225}\end{align}\)

(iii) \(\begin{align} 0.3796\end{align}\)

iii) \(\begin{align}0.3796\end{align}\)

iv) \(\begin{align}7.478478 \ldots . . . .=7. \overline{478}\end{align}\)

v) \(\begin{align}1.101001000100001\end{align}\)

 

 Video Solution
Number Systems
Ex 1.3 | Question 9

Text Solution

Steps:

i) \(\begin{align}\sqrt {23} = \frac{{\sqrt {23} }}{1} = \frac{p}{q},\end{align}\) but \(p\) is not an integer.

Hence \(\begin{align}{\sqrt{23}}\end{align}\) is an irrational number.

ii) \(\begin{align} \sqrt {225} = \frac{{15}}{1} = \frac{p}{q},\end{align}\) where \(p\) and \(q\) are integers. \(\begin{align}q \ne 0.\end{align}\)

Hence \(\begin{align}\sqrt {225} \end{align}\) is a rational number.

iii) \(\begin{align}0.3796\end{align}\)

\(\begin{align}0.3796\end{align}\) is a rational number . Because it is a terminating decimal number.

iv) \(\begin{align}7.478478 \ldots . . . .=7. \overline{478}\end{align}\)

It is an rational number. As It is a non-terminating recurring decimal.

v) \(\begin{align}1.101001000100001\end{align}\)

It is an irrational number because it is a non-terminating and non-recurring decimal. 

  
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