Class 9 Rational and Irrational Numbers — practice questions with answers

Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which of the following is a rational number?

A $2$
B $\frac{5}{7}$
Cpi
D $3$

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Answer: B)

\frac{5}{7}

A rational number can be written as

\frac{p}{q}

with q not 0.

\frac{5}{7}

is of this form, so it is rational.

2

3

and pi are irrational.

2. Simplify

50

and state its nature.

A $52$ , irrational
B $252$ , rational
C $52$ , rational
D $105$ , irrational

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Answer: A)

52

, irrational

50

25 \times 2

52

. Since

2

is irrational,

52

is irrational.

3. A square garden has area 9 sq m. The side length is a rational number. What is the side (in m)?

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Answer: C) 3

Side =

9

= 3 m. Since 9 is a perfect square, the side is rational.

4. Find a rational number and an irrational number between 0.1 and 0.2.
Which option lists a valid (rational, irrational) pair in that interval?

A(0.15 , 0.150150015000... non-recurring)
B(0.15 , 0.1212... recurring)
C( $0.02$ , 0.18)
D(0.05 , 0.25)

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Answer: A) (0.15 , 0.150150015000... non-recurring)

0.15 is rational and lies between 0.1 and 0.2. 0.150150015000... is non-terminating non-recurring (irrational) and also lies in the interval. The other options either give recurring (rational) second entries or values outside the interval.

5. If

x = 7 + 43

, find the value of

x + \frac{1}{x}

.
(Hint: rationalise

\frac{1}{x}

first.)

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Answer: A) 14

\frac{1}{x} = \frac{1}{7 + 4 3}

. Multiply by conjugate

(7 - 43)

: denominator = 49 - 48 = 1, so

\frac{1}{x} = 7 - 43

. Then

x + \frac{1}{x} = (7 + 43) + (7 - 43) = 14

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