Real Numbers Questions and Answers: Practice Problems with Detailed Solutions

Real Numbers Questions and Answers are available in this Maths article. Real Numbers Questions and Answers are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Real Numbers. Real numbers include whole numbers, fractions and decimals which we use in our day to day life.

Table of Contents

• What are Real Numbers?
• Real Numbers vs. Other Sets
• Real Numbers Questions and Answers
• Practice Questions on Real Numbers

What are real numbers?

Real numbers are all the numbers you can write on a number line. They include positive numbers, negative numbers, and zero. Real numbers also include fractions and decimals. If you can measure something, you can use a real number.

Also Check: 

• Real Numbers
• Important Questions on Real Numbers - Class 10
  
  

Real Numbers vs. Other Sets

Set	Includes	Example
Natural Numbers	Positive integers	1, 2, 3...
Whole Numbers	0 and natural numbers	0, 1, 2, 3...
Integers	Positive, negative, zero	..., -1, 0, 1...
Rational Numbers	Fractions of integers	1/2, 0.5, -3
Real Numbers	All of above + irrational	π, √2, e, 0.5...

Real Numbers Questions and Answers

1. What are real numbers?

Answer: Real numbers are all the numbers that can be shown on a number line. They include:

• Natural numbers
• Whole numbers
• Integers
• Rational numbers
• Irrational numbers

Examples: 2, -5, 0, 3/4, √2, π

2. Is √25 a real number?

Answer: Yes, √25 is a real number because:

25=5

Since 5 lies on the number line, it is a real number.

3. Is π (pi) a rational or irrational number?

Answer: π is an irrational number because its decimal form never ends and never repeats.

Approximate value:

π≈3.14159

4. Find the HCF of 18 and 24.

Answer:
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Common factors = 1, 2, 3, 6

Therefore, the HCF is:HCF(18,24)=6

5. Find the LCM of 12 and 15.

Answer: Prime factorization:

12 = 2 × 2 × 3

15 = 3 × 5

LCM = 2 × 2 × 3 × 5

LCM(12,15)=60

6. Is 0 a real number?

Answer: Yes, 0 is a real number because it exists on the number line and belongs to the set of whole numbers and integers.

7. Convert 0.75 into a fraction.

Answer:0.75=75100=34

So, 0.75 as a fraction is 3/4.

8. Find the square root of 144.

Answer:144=12

Therefore, the square root of 144 is 12.

9. Are negative numbers real numbers?

Answer: Yes, negative numbers are real numbers because they can be represented on the number line.

Examples: -1, -5, -20

10. State the Euclid Division Lemma.

Answer: The Euclid Division Lemma states that for any two positive integers (a) and (b):

a=bq+r,0≤r<b

Where:

• (a) = dividend
• (b) = divisor
• (q) = quotient
• (r) = remainder

Read more: Class 9 - Operations on Real Numbers

Practice Questions on Real Numbers

1. Identify whether the following numbers are rational or irrational:

• (7)
• (58)
• (π)
• (0.333…)

2. Find the HCF of 36 and 48 using prime factorization.

3. Find the LCM of 20 and 30.

4. Express the decimal number 0.125 as a fraction in simplest form.

5. Find the square root of 196.

196

6. Check whether the number (81) is a real number.

7. Using Euclid’s Division Lemma, divide 29 by 5 and find:

• Quotient
• Remainder

a=bq+r,0≤r<b

8. Write any five examples of integers and real numbers.

9. Simplify the following:

49+64

10. Determine whether the following statement is true or false:

“Every whole number is a real number.”