Number Systems Class 9 Maths — Revision Notes
This chapter covers rational and irrational numbers, their properties, and operations. Students learn about number line and decimal representation of numbe
TL;DR: This chapter covers rational and irrational numbers, their properties, and operations. Students learn about number line and decimal representation of…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter covers rational and irrational numbers, their properties, and operations. Students learn about number line and decimal representation of numbe
Rational Numbers
- Rational number is number that can be expressed as p/q where p and q are integers and q ≠ 0
- All integers are rational (n = n/1)
- Decimal form is terminating or non-terminating repeating
- Rational numbers are dense on number line
Irrational Numbers
- Irrational number cannot be expressed as p/q
- Decimal form is non-terminating non-repeating
- Examples: sqrt(2), sqrt(3), π, e
- Sum/difference of rational and irrational is irrational
Real Numbers
- Real numbers include all rational and irrational numbers
- Real numbers form continuous number line
- Every real number corresponds to unique point on number line
- Operations on real numbers follow closure, commutative, associative properties
Surds
- Surd is irrational root of rational number
- sqrt(2), sqrt(3), ∛2 are surds
- Like surds: surds with same radicand (sqrt(2) and 3sqrt(2))
- Simplification: sqrt(ab) = sqrt(a) x sqrt(b) (for positive a, b)
Key Terms
- Rational Number: Number expressible as p/q where p and q are integers
- Irrational Number: Number that cannot be expressed as p/q
- Surd: Irrational root of a rational number
Frequently Asked Questions
Prove that sqrt(2) is irrational.
Assume sqrt(2) = p/q (lowest terms). Then 2q^2 = p^2, so p^2 is even, p is even. Let p = 2k, then q^2 = 2k^2, so q is even. Both are even, contradicting assumption.
How do you rationalize denominator?
Multiply numerator and denominator by conjugate. For 1/(sqrt(2)+1), multiply by (sqrt(2)-1)/(sqrt(2)-1) to get (sqrt(2)-1)/(2-1) = sqrt(2)-1.
More Class 9 Maths Revision Notes
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →