Decimal Representation of a Rational and Irrational Number

Q.

What is $2.25$ as a fraction?

Q. There are infinitely many irrational numbers between any two rational numbers.

1. True
2. False

Q.

Write each of the following as decimals: $200+60+5+\frac{1}{10}$.

Q.

Write the following as decimal:

$\frac{55}{10}$

Q.

Select the correct option about the numbers given below.

(i) √27

(ii) √256

(iii) 0.3796

(iv) 7.478478...

(v) 1.101001000100001...

1. (i) and (v) are irrational

2. only (v) is irrational

3. (iv) and (v) is irrational

4. none are irrational

Q.

Write ­$\frac{3}{5}$as decimal number.

Q.

Which one of the following numbers is a non-terminating and repeating decimal?

1. $\frac{39}{24}$

2. $\frac{78}{32}$

3. $\frac{49}{56}$

4. $\frac{3}{11}$

Q. Convert $\frac{4}{11}$ into decimal form.

1. $0.\overline{36}$
2. $18.\overline{36}$
3. $36.\overline{36}$
4. $0.37\overline{36}$

Q. Which of the following fractions has a non-terminating decimal expansion?

1. 77/210
2. 17/8
3. 35/50
4. 23/8

Q.

A fraction $\frac{13}{20}$ is equal to the decimal

1. 1.3

2. 0.65

3. 6.5

4. none of these

Q. The number $15.\overline{65987}$ is ______.

1. rational
2. irrational
3. terminating
4. non-terminating
5. recurring
6. non-recurring
7. integer
8. greater than 15
9. 15.6598765987...
10. whole number

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. 3.27272727... is ____________.

1. an integer
2. a rational number
3. a natural number
4. an irrational number

Q. A given number is irrational in nature if and only if the decimal representation is ___.

1. non terminating
2. terminating
3. non terminating, non repeating
4. non terminating, repeating

Q.

Which one of the following is a correct statement?

1. Decimal expansion of an irrational number is repeating.

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

3. Decimal expansion of an irrational number is terminating

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

Q. The decimal representation of a rational number is ___ in nature.

1. non terminating, non repeating
2. recurring
3. terminating
4. terminating or recurring