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CBSE - Class 10 Mathematics Real numbers Worksheet

Fill in the blanks: 5/12 ÷ (_____) = -35/18

A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?

2 and 3

3 and 5

2, 3 and 5

2 and 5

If HCF and LCM of two numbers is 5 and 50 respectively ,then numbers are

10 and 25

5 and 50

12 and 25

10 and 20

If LCM(x, 18) =36 and HCF(x, 18) =2, then x is

Simplify: 2/3 + -4/5 + 7/15 + -11/20

The sum or difference of a rational and an irrational number is

always irrational

always rational

rational or irrational

none of these

987/10500 will have

terminating deimal expansion

Non-terminating and Non-repeating deimal expansion

Non-terminating repeating deimal expansion

None of these

If a number has prime factorisation 2^m × 5^n, its decimal expansion is:

Non-terminating

Terminating

Non-repeating

Irrational

The decimal expansion of the rational number $\frac{33}{2^{2}\times 5}$ will terminate after

one decimal place

two decimal places

three decimal places

more than 3 decimal places

10.

Fill in the blanks: The value of {-8/13 × 26/-3} is _____

11.

For all a,b belong R, $a \neq 0, b\neq 0, a> b$ this imply

a. a < b b. a = b c. 1/a < 1â??b d. 1â??a > 1â??b

12.

The decimal expansion of the rational number $\small \frac{14587}{1250}$ will terminate after

one decimal place

two decimal place

three decimal place

four decimal place

13.

There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

14.

Fill in the blanks: The decimal form of irrational number is neither _____ or _____

15.

The smallest number by which √27 should be multiplied so as to get a rational number is

√27

√3

3√3

16.

Prove that $6 + 10\sqrt{11}$ is an irrational number.

17.

Decimal expansion of a rational numer is

always terminating

always non-terminating

either terminating or non-terminating recurring

none of these

18.

Such two numbers are possible which LCM is 50 and HCF is 7.

a. True b. False

19.

Choose the correct option: Euclid’s division algorithm can be applied to _______.

a. only positive integers b. only negative integers c. all integers d. all integers except 0.

20.

If a² = 23/25, then a is

Rational

Irrational

Whole number

Integer

Worksheet Answers

-0.21428571430000001

Option D

Option A

Option C

-0.21666666670000001

Option A

Option B

Solution:

Only factors 2 and 5 → terminating decimal.

Option B

10.

5.33

11.

Option C

12.

Option D

13.

Option B

Solution:

HCF of 312, 260, 156 = 52

14.

Recurring or Terminating

15.

Option C

16.

Let's assume that $6 + 10\sqrt{11}$ is a rational number Therefore, we can f ind two integers and b, such that $6 + 10\sqrt{11}$ = a/b where,b is not equal to zero.Now, $\sqrt{11} = \frac{6}{10} + \frac{1}{10b}$ . Now, $\sqrt{11} = 6b + \frac{a}{10b}$ .Since a and b are integers, (6b + a) and (10b) are also integers. Thus 6b+a/10b is rational hence, $\sqrt{11}$ should also be rational. This contradicts the f act that $\sqrt{11}$ is irrational.Theref ore, our assumption is f alse and hence, $6 + 10\sqrt{11}$ is irrational.

17.

Option C

18.

Option B

19.

Option A

20.

Option B

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