Decimal Expansion of Rational and Irrational Numbers

Q.

Find the hypotenuse of a right angled triangle whose perpendicular sides are $\sqrt{6}$ cm and $\sqrt{3}$ cm.

1. 2 cm

2. 4 cm

3. 3 cm

4. 1 cm

Q.

The numbers which have a non-terminating and non-repeating decimal expansion and cannot be represented in the form of $\frac{p}{q}$ ( q is not equal to '0') are known as

___ numbers.

Q.

Which of the following fractions is a terminating decimal?

1. $\frac{1}{6}$

2. $\frac{1}{3}$

3. $\frac{1}{5}$

4. $\frac{1}{7}$

Q.

A number ${}^{\prime }{x}^{\prime }$was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

1. 11

2. 13

3. 14

4. 12

Q.

The decimal form of $\frac{7}{8}$ is _.

1. 2.1875

2. 0.45

3. 1.234

4. 0.875

Q.

Which one of the following is a correct statement?

1. Decimal expansion of an irrational number is non-terminating and non-repeating

2. Decimal expansion of an irrational number is terminating

3. Decimal expansion of an irrational number is repeating.

4. Decimal expansion of a rational number is always non-terminating

Q.

Which of the following fraction is terminating decimal?

1. 

2. 

3. 

4. 

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. i) and iv)
2. All of the above
3. Only iv)
4. ii) and iii)

Q.

Which of the following is a recurring decimal?

a)4.171717.....

b)5.131131131......

c)6.989989989989......

[3 Marks]

1. c
2. All of the above
3. a
4. b

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. ii) and iii)
2. Only iv)
3. i) and iv)
4. All of the above