Mathematics is one of the most scoring and interesting subjects for Class 9 students. Understanding the need for regular practice, we have provided detailed RD Sharma Class 9 Solutions for students. These solutions help them master concepts easily.
Chapter 1 – Number System in RD Sharma Class 9 Maths covers all important concepts like rational numbers, irrational numbers, and real numbers, making it easier for students to understand the number sytem concept easily.
By practicing a variety of questions from RD Sharma, students not only gain concept clarity but also improve their confidence in solving tough problems. Regular practice with these questions will help in exam preparation and helps students can handle even tricky questions in the class 9th exam with ease.
RD Sharma Solutions Class 9 Maths Chapter 1 Number System PDF Download
Students can easily download the PDF of RD Sharma Class 9 Maths Solutions for Chapter 1 from the link below and practice questions whenever they feel confident with their NCERT textbook exercises.
It is always recommended that students treat RD Sharma as a supplementary book. Start with NCERT for concept clarity, and once the basics are strong, move on to RD Sharma for extra practice and deeper understanding. This approach will help students in clearing every topic in a crystal-clear way.
This RD Sharma Solutions for Class 9 Maths Chapter 1 PDF is updated for the 2025-26 academic year, fully aligned with the latest CBSE syllabus, and carefully prepared by our expert faculty. The solutions are checked for accuracy, making them a reliable study resource for students. They can use it for their daily practice and exam preparation.
Download RD Sharma Number System Class 9 PDF with Answers
RD Sharma Solutions Class 9 Maths Chapter 1 Number System Exercise Solutions
Exercise 1.1
Q1. Is Zero a Rational Number? Explain.
Yes, zero is definitely a rational number because it can be written in the form 0/q, where q is any non-zero integer.
Example — 0/1, 0/5, 0/100
Q2. Find Five Rational Numbers Between 1 and 2.
We find rational numbers by averaging step by step:
Between 1 and 2 → (1 + 2) ÷ 2 = 3/2
Between 1 and 3/2 → (1 + 3/2) ÷ 2 = 5/4
Between 1 and 5/4 → (1 + 5/4) ÷ 2 = 9/8
Between 3/2 and 2 → (3/2 + 2) ÷ 2 = 7/4
Between 7/4 and 2 → (7/4 + 2) ÷ 2 = 15/8
Answer: The five rational numbers are 9/8, 5/4, 3/2, 7/4, 15/8
Q3. Find Six Rational Numbers Between 3 and 4.
Multiply both numbers by 7 (as we need 6 numbers, use n+1 = 7):
3 × 7/7 = 21/7, 4 × 7/7 = 28/7
Now pick numbers between 21/7 and 28/7:
22/7, 23/7, 24/7, 25/7, 26/7, 27/7
Q4. Find Five Rational Numbers Between 3/5 and 4/5.
Multiply both by 6/6 (n+1 = 6):
3/5 × 6/6 = 18/30, 4/5 × 6/6 = 24/30
Numbers between them are: 19/30, 20/30, 21/30, 22/30, 23/30
Q5. True or False with Reason:
(i) Every whole number is a natural number. ✗ False (0 is not a natural number)
(ii) Every integer is a rational number. ✓ True
(iii) Every rational number is an integer. ✗ False (Example: 1/2 is rational but not an integer)
(iv) Every natural number is a whole number. ✓ True
(v) Every integer is a whole number. ✗ False (Negative integers are not whole numbers)
(vi) Every rational number is a whole number. ✗ False (Fractions like 2/3 are not whole numbers)
Exercise 1.2 — Decimal Form Answers
Q1. Express as Decimal:
(i) 42/100 = 0.42
(ii) 327/500 = 0.654
(iii) 15/4 = 3.75
Q2. Express as Decimal:
(i) 2/3 = 0.666… (Repeating)
(ii) -4/9 = -0.444…
(iii) -2/15 = -0.133…
(iv) -22/13 ≈ -1.692…
(v) 437/999 ≈ 0.437437437… (Repeating)
(vi) 33/26 ≈ 1.269…
Exercise 1.3 — Express as Fraction (p/q)
Q1. Convert to Fraction:
(i) 0.39 = 39/100
(ii) 0.750 = 3/4
(iii) 2.15 = 43/20
(iv) 7.010 = 701/100
(v) 9.90 = 99/10
(vi) 1.0001 = 10001/10000
Q2. Recurring Decimals to Fractions (Examples):
(i) 0.4̅ = 4/9
(ii) 0.3737… = 37/99
(iii) 0.5454… = 54/99
(iv) 0.621621… = 621/999 = 23/37 (Simplified)
(v) 125.333… = 376/3
(vi) 4.7777… = 43/9
(vii) 0.47777… = 43/90
Exercise 1.4 — Irrational Numbers & Properties
Q1. Define an Irrational Number:
A number that cannot be written as p/q where p and q are integers (q ≠ 0) is called an irrational number. Its decimal expansion is non-terminating and non-repeating. Example — √2
Q2. Difference Between Rational and Irrational Numbers:
Rational numbers can be expressed as a fraction (like 2/3) and have terminating or repeating decimals.
Irrational numbers cannot be written as a fraction and have non-terminating, non-repeating decimals. Example — √3
Q3. Rational or Irrational — Check:
(i) √7 — Irrational
(ii) √4 — Rational (2)
(iii) 2 + √3 — Irrational
(iv) √3 + √2 — Irrational
(v) √3 + √5 — Irrational
(vi) (√2 – 2)² = 6 – 4√2 — Irrational
(vii) (2 – √2)(2 + √2) = 2 — Rational
(viii) (√3 + √2)² = 5 + 2√6 — Irrational
(ix) √5 – 2 — Irrational
(x) √23 — Irrational
(xi) √225 = 15 — Rational
(xii) 0.3796 — Rational
(xiii) 7.478478… — Rational
(xiv) 1.1010010001… — Irrational
Q4. Identify and Decimal Representation:
(i) √4 = 2.0 — Rational
(ii) 3√18 — Irrational
(iii) √1.44 = 1.2 — Rational
(iv) √9/27 = 1/√3 — Irrational
(v) –√64 = –8.0 — Rational
(vi) √100 = 10.0 — Rational
Q5. Which Variables are Rational or Irrational?
(i) x² = 5 → x = √5 — Irrational
(ii) y² = 9 → y = 3 — Rational
(iii) z² = 0.04 → z = 0.2 — Rational
(iv) u² = 17/4 → u = √17/2 — Irrational
(v) v² = 3 → v = √3 — Irrational
(vi) w² = 27 → w = 3√3 — Irrational
(vii) t² = 0.4 → t = 2/√10 — Irrational
Important Concept of RD Sharma Class 9 Maths Chapter 1 — Number System
- Types of numbers — natural, whole, integers, rational, and irrational.
- Representing numbers on the number line.
- Finding rational numbers between two given numbers.
- Decimal expansion — terminating and non-terminating repeating decimals.
- Properties of irrational numbers.
- Laws of exponents for real numbers.
- Simplifying expressions with roots and exponents.
- Comparing and classifying different numbers.
- Finding square roots and cube roots of real numbers.
- Application of number system concepts in daily life.