Class 9 Maths Chapter 1 Number Systems – Exercise 1.3 NCERT Solutions

Introduction

Exercise 1.3 helps you understand decimal expansions of rational numbers. You’ll learn how to check if a fraction has a terminating decimal or a repeating decimal, based on its denominator.

Key Formula Used

• If a rational number is in the form $\frac{p}{q}$ (where $p,q$ are integers and $q\mathrm{\ne }0$):

  • Decimal expansion terminates if the prime factors of $q$ are only 2 and/or 5.

  • Decimal expansion is non‑terminating repeating if $q$ has any prime factor other than 2 or 5.

Solved Questions (Step by Step)

Q1. Express $\frac{10}{3}$ in decimal form.

Solution:

• Divide 10 by 3: $10÷3=\mathrm{3.333...}$.

• Decimal expansion is non‑terminating repeating.

Q2. Express $\frac{7}{8}$ in decimal form.

Solution:

• Divide 7 by 8: $7÷8=0.875$.

• Decimal expansion terminates.

Q3. Express $\frac{1}{7}$ in decimal form.

Solution:

• Divide 1 by 7: $\mathrm{0.142857142857...}$.

• Decimal expansion is non‑terminating repeating.

Q4. Express $\frac{3}{13}$ in decimal form.

Solution:

• Divide 3 by 13: $\mathrm{0.230769230769...}$.

• Decimal expansion is non‑terminating repeating.

Q5. Express $\frac{2}{5}$ in decimal form.

Solution:

• Divide 2 by 5: $0.4$.

• Decimal expansion terminates.

Q6. Express $\frac{11}{2}$ in decimal form.

Solution:

• Divide 11 by 2: $5.5$.

• Decimal expansion terminates.

Q7. Express $\frac{15}{8}$ in decimal form.

Solution:

• Divide 15 by 8: $1.875$.

• Decimal expansion terminates.

Q8. Express $\frac{29}{12}$ in decimal form.

Solution:

• Divide 29 by 12: $\mathrm{2.41666...}$.

• Decimal expansion is non‑terminating repeating.

Q9. Express $\frac{57}{50}$ in decimal form.

Solution:

• Divide 57 by 50: $1.14$.

• Decimal expansion terminates.

Q10. Express $\frac{23}{2}$ in decimal form.

Solution:

• Divide 23 by 2: $11.5$.

• Decimal expansion terminates.

Q11. Express $\frac{29}{5}$ in decimal form.

Solution:

• Divide 29 by 5: $5.8$.

• Decimal expansion terminates.

Q12. Express $\frac{31}{3}$ in decimal form.

Solution:

• Divide 31 by 3: $\mathrm{10.333...}$.

• Decimal expansion is non‑terminating repeating.

Q13. Express $\frac{18}{125}$ in decimal form.

Solution:

• Divide 18 by 125: $0.144$.

• Decimal expansion terminates.

Q14. Express $\frac{45}{7}$ in decimal form.

Solution:

• Divide 45 by 7: $\mathrm{6.428571...}$.

• Decimal expansion is non‑terminating repeating.

Q15. Express $\frac{77}{210}$ in decimal form.

Solution:

• Simplify denominator: 210 = $2\times 3\times 5\times 7$.

• Since denominator has primes other than 2 and 5, decimal expansion is non‑terminating repeating.

Conclusion

Exercise 1.3 has 15 questions that train you to identify whether a rational number’s decimal expansion terminates or repeats. This skill is crucial for understanding number systems and later topics in algebra.

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