Real Numbers Worksheet Class 10

In Class 10 Maths, the chapter on Real Numbers is fundamental. Real numbers include all the numbers you can think of, like whole numbers, fractions, and decimals.

Euclid’s Division Lemma: It states that for any two positive integers a and b, there exist whole numbers q and r such that a = bq + r, where 0 ≤ r < b. This helps in finding the highest common factor (HCF) of two numbers.

Prime Numbers: These are numbers greater than 1 with no divisors other than 1 and themselves. For example, 2, 3, 5, and 7 are prime numbers.

Composite Numbers: These numbers have more than two divisors. For example, 4, 6, and 8 are composite numbers.

Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorized) as a product of prime numbers, and this factorization is unique, apart from the order of the factors.

Irrational Numbers: These cannot be expressed as a simple fraction. Their decimal form is non-terminating and non-repeating. For example, √2 and π are irrational numbers.

Rational Numbers: These can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.

Understanding real numbers helps in solving problems related to HCF, LCM, and different properties of numbers, forming a foundation for higher mathematical concepts.

Class 10 Math Polynomials Worksheets

Real Numbers Worksheet Class 10 PDF

Real Numbers Worksheet Class 10

Real Numbers Worksheet Class 10 – Practice Question with Answers

Worksheet 1: Real Numbers Basics

Answer the following questions.

1. Define a real number.
2. Identify the type of number:
   $\sqrt{2}$

    

   2​

3. Simplify:
   $\sqrt{49}$

    

   49​

4. Write the decimal expansion of
   $\frac{1}{4}$

    

   41​.

5. Are all integers real numbers? Explain.

Answers:

1. A real number is any number that can be found on the number line, including both rational and irrational numbers.
2. 
   $\sqrt{2}$

    

   2​ is an irrational number.

3. 
   $\sqrt{49} = 7$

    

   49​=7

4. 
   $\frac{1}{4} = 0.25$

    

   41​=0.25

5. Yes, all integers are real numbers because they can be found on the number line.

Worksheet 2: Rational and Irrational Numbers

Instructions: Classify the following numbers as rational or irrational.

1. 
   $3.5$

    

   3.5

2. 
   $\pi$

    

   π

3. 
   $0$

    

   0

4. 
   $\sqrt{10}$

    

   10​

5. 
   $\frac{7}{3}$

    

   37​

Answers:

1. Rational
2. Irrational
3. Rational
4. Irrational
5. Rational

Worksheet 3: Decimal Expansions

Instructions: Determine whether the decimal expansion is terminating or non-terminating.

1. 
   $0.375$

    

   0.375

2. 
   $1.3333…$

    

   1.3333…

3. 
   $0.6666…$

    

   0.6666…

4. 
   $0.5$

    

   0.5

5. 
   $0.142857…$

    

   0.142857… (repeating)

Answers:

1. Terminating
2. Non-terminating
3. Non-terminating
4. Terminating
5. Non-terminating (repeating)

Worksheet 4: Operations with Real Numbers

Instructions: Perform the following operations.

1. 
   $5 + \sqrt{16}$

    

   5+16​

2. 
   $\frac{3}{4} \times 2$

    

   43​×2

3. 
   $7 – \sqrt{49}$

    

   7−49​

4. 
   $\frac{8}{2} + \sqrt{9}$

    

   28​+9​

5. 
   $\sqrt{25} \times 2$

    

   25​×2

Answers:

1. 
   $5 + 4 = 9$

    

   5+4=9

2. 
   $\frac{3}{4} \times 2 = \frac{3 \times 2}{4} = \frac{6}{4} = 1.5$

    

   43​×2=43×2​=46​=1.5

3. 
   $7 – 7 = 0$

    

   7−7=0

4. 
   $\frac{8}{2} + 3 = 4 + 3 = 7$

    

   28​+3=4+3=7

5. 
   $\sqrt{25} \times 2 = 5 \times 2 = 10$

    

   25​×2=5×2=10

Worksheet 5: Properties of Real Numbers

Instructions: Fill in the blanks.

1. The sum of a rational number and an irrational number is __________.
2. The product of two irrational numbers is __________.
3. Every real number has a __________ representation on the number line.
4. The square root of any non-perfect square is __________.
5. Real numbers include __________ and __________ numbers.

Answers:

1. Irrational
2. Rational or irrational (depends on the numbers)
3. Unique
4. Irrational
5. Rational, irrational