Class 9 Maths - CBSE
Number Systems
The Number Systems chapter for Class 9 CBSE builds the foundation of algebra by extending the number line from rational numbers to real numbers. Students learn to classify numbers into natural numbers, integers, rational numbers, and irrational numbers. Key topics include decimal expansions of rational numbers, representing irrational numbers like root 2 on a number line, operations on real numbers, and the process of rationalizing the denominator. This chapter is vital for board exams as it tests conceptual clarity and foundational algebra skills, typically carrying around 6 to 8 marks in the Class 9 annual mathematics examination.
Start Learning FreeKey Concepts
Rational Numbers
Numbers that can be expressed in the form p/q, where p and q are integers and q is not equal to zero.
Irrational Numbers
Numbers that cannot be written in the form p/q and have non-terminating and non-recurring decimal expansions, such as root 2 and pi.
Real Numbers
The collection of all rational and irrational numbers that together fill the entire number line.
Decimal Expansions
The representation of real numbers in decimal form, which can be terminating, non-terminating recurring, or non-terminating non-recurring.
Rationalisation
The process of converting an irrational denominator into a rational number by multiplying the numerator and denominator by a suitable rationalising factor.
Important Formulas
Board Exam Info
In the CBSE Class 9 Mathematics examination, the Number Systems chapter falls under the 'Number Systems' unit, which usually carries 6 to 8 marks. Common question types include converting decimals of the form p/q, rationalizing denominators with binomial surds, simplifying expressions using laws of exponents, and locating irrational numbers on the number line.
Frequently Asked Questions
Is zero a rational number?
Yes, zero is a rational number because it can be written as p/q where p = 0 and q is any non-zero integer, such as 0/1 or 0/5.
How do I convert a recurring decimal like 0.333... into p/q form?
Let x = 0.333... Then multiply both sides by 10 to get 10x = 3.333... Subtract x from 10x to get 9x = 3, which gives x = 3/9 or 1/3.
What is the difference between rational and irrational numbers?
Rational numbers have decimal expansions that either terminate or repeat, whereas irrational numbers have decimal expansions that are neither terminating nor repeating.
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