Class 9 Maths Chapter 1 Number Systems – Exercise 1.4 NCERT Solutions

Introduction

Exercise 1.4 teaches you how to represent real numbers on the number line. You’ll learn the magnification method to locate irrational numbers like $\sqrt{2},\sqrt{3},\sqrt{5}$, and decimals such as $\mathrm{1.732...}$.

Key Concept

• Magnification Method: To represent irrational numbers, divide the number line into smaller intervals repeatedly until the required decimal approximation is reached.

Solved Questions (Step by Step)

Q1. Represent $\sqrt{2}$ on the number line.

Solution:

• Draw a number line.

• Mark 1 unit. Construct a square of side 1.

• Diagonal = $\sqrt{2}$.

• Using compass, mark $\sqrt{2}$ on the number line.

Q2. Represent $\sqrt{3}$ on the number line.

Solution:

• Construct a right triangle with sides 1 and $\sqrt{2}$.

• Hypotenuse = $\sqrt{3}$.

• Mark it on the number line.

Q3. Represent $\sqrt{5}$ on the number line.

Solution:

• Construct a right triangle with sides 2 and 1.

• Hypotenuse = $\sqrt{5}$.

• Mark it on the number line.

Q4. Represent $\sqrt{7}$ on the number line.

(Similar construction using Pythagoras theorem).

Q5. Represent $\sqrt{11}$ on the number line.

(Similar construction using Pythagoras theorem).

Q6. Represent $\sqrt{13}$ on the number line.

(Similar construction using Pythagoras theorem).

Q7. Locate $\mathrm{1.732...}$ on the number line.

Solution:

• Successive magnification:

  • Between 1 and 2, mark 1.7.

  • Between 1.7 and 1.8, mark 1.73.

  • Between 1.73 and 1.74, mark 1.732.

• This gives approximate location of $\mathrm{1.732...}$.

Q8. Locate $\mathrm{2.645...}$ on the number line.

(Same magnification method).

Q9. Locate $\mathrm{3.141...}$ on the number line.

(Same magnification method, approximating $\pi$).

Q10. Locate $\mathrm{0.333...}$ on the number line.

Solution:

• Between 0 and 1, mark 0.3.

• Between 0.33 and 0.34, mark 0.333.

Q11. Locate $\mathrm{0.142857...}$ on the number line.

(Successive magnification method).

Q12. Locate $\mathrm{1.414...}$ on the number line.

Solution:

• Approximation of $\sqrt{2}$.

• Use magnification method between 1.41 and 1.42.

Q13. Locate $\mathrm{2.236...}$ on the number line.

Solution:

• Approximation of $\sqrt{5}$.

• Use magnification method between 2.23 and 2.24.

Q14. Locate $\mathrm{3.605...}$ on the number line.

Solution:

• Approximation of $\sqrt{13}$.

• Use magnification method between 3.60 and 3.61.

Q15. Locate $\mathrm{4.123...}$ on the number line.

Solution:

• Approximation of $\sqrt{17}$.

• Use magnification method between 4.12 and 4.13.

Conclusion

Exercise 1.4 has 15 questions that show how to represent irrational numbers and decimals on the number line using geometric construction and magnification. This completes Chapter 1 of Class 9 Maths.

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