Class 9 Maths - BIHAR
Number Systems
The Number Systems chapter in Class 9 Mathematics introduces students to the expansion of numbers beyond fractions and integers. It covers rational and irrational numbers, real numbers and their decimal expansions, representing real numbers on the number line through successive magnification, operations on real numbers, and the laws of exponents for real numbers. This foundational chapter is crucial for the Bihar School Examination Board (BSEB) exams as it builds the base for algebra and higher-level mathematics. Questions from this chapter frequently appear as objective, short-answer, and long-answer problems, making it a high-scoring area for board aspirants.
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 together forms the set of real numbers, which completely fill the number line.
Decimal Expansions
Rational numbers have either terminating or non-terminating recurring decimal expansions, whereas irrational numbers have non-terminating non-recurring expansions.
Rationalisation
The process of converting an irrational denominator into a rational number by multiplying the numerator and denominator by a suitable conjugate factor.
Laws of Exponents
Algebraic rules governing powers of real numbers, such as a^m * a^n = a^(m+n) and (a^m)^n = a^(m*n).
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 9 Mathematics annual examination, the Number Systems chapter typically carries around 6 to 10 marks. Common question types include multiple-choice questions on rational and irrational identification, numerical problems on rationalising the denominator, simplifying exponential expressions, and proving numbers to be irrational.
Frequently Asked Questions
Is zero a rational number?
Yes, zero is a rational number because it can be written in the form p/q as 0/1, where p and q are integers and q is not equal to zero.
How can we prove that root 2 is an irrational number?
We can prove it using the method of contradiction by assuming it is rational, expressing it in its simplest fraction form, and showing that it leads to a mathematical contradiction.
What is the difference between terminating and non-terminating repeating decimals?
A terminating decimal comes to an end after a finite number of decimal places (like 0.25), whereas a non-terminating repeating decimal goes on forever but has a repeating block of digits (like 0.333...).
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