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CBSE class 9 Mathematics Chapter 1 Number Systems notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Number Systems class 9 Notes latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 9 Mathematics notes on Chapter 1 Number Systems are also available for download in CBSE Guide website.

CBSE Guide Number Systems class 9 Notes

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9 Mathematics notes Chapter 1 Number Systems

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CBSE Class 09 Mathematics
Revision Notes
CHAPTER – 1
NUMBER SYSTEMS

1 Rational Numbers

2 Irrational Numbers

3 Real Numbers and their Decimal Expansions

4 Operations on Real Numbers

5 Laws of Exponents for Real Numbers

Natural numbers are : 1, 2, 3, …………….. denoted by N.
Whole numbers are : 0, 1, 2, 3, ……………… denoted by W.
Integers : ……. -3, -2, -1, 0, 1, 2, 3, ……………… denoted by Z.
Rational numbers – All the numbers which can be written in the form ${p \over q}$ are called rational numbers where p and q are integers and $q \ne 0.$ Every integer p is also a rational number, can be written as ${p \over 1}.$
Irrational numbers – A number is called irrational, if it cannot be written in the form ${p \over q}$ where p and q are integers and $q \ne 0.$
The decimal expansion of a rational number is either terminating or non terminating recurring. Thus we say that a number whose decimal expansion is either terminating or non terminating recurring is a rational number.
Terminating decimals: The rational numbers with a finite decimal part or for which the long division terminates after a finite number of steps are known as finite or terminating decimals.
Non-Terminating decimals: The rational numbers with an infinite decimal part or for which the long division does not terminate even after an infinite number of steps are known as infinite or non-terminating decimals
The decimal expansion of a irrational number is non terminating non recurring.
All the rational numbers and irrational numbers taken together make a collection of real numbers.
A real number is either rational or irrational.
If r is rational and s is irrational then r+s, r–s, r.s are always irrational numbers but ${r \over s}$ may be rational or irrational.
If n is a natural number other than a perfect square, then $\sqrt n$ is a irrational number.
Negative of an irrational number is an irrational number.
There is a real number corresponding to every point on the number line. Also, corresponding to every real number there is a point on the number line.
Every irrational number can be represented on a number line using Pythagoras theorem.
For every positive real number $x,$ $\sqrt x$ can be represented by a point on the number line by using the following steps:

Obtain all positive real numbers $x$ (say).
Draw a line and mark a point P on it.
Make a point Q on the line such that PQ = $x$ units.
From point Q marka distance of 1 unit and mark the new point as R.
Find the mid-point of PR and mark the point as O.
Draw a circle with centre O and radius OR.
Draw a line perpendicular to PR passing through Q and intersecting the semi-circle at S. Length QS is equal to $\sqrt x$

Rationalization means to remove square root from the denominator.

$\frac{{3 + \sqrt5 }}{{\sqrt 2 }}$ to remove we will multiply both numerator & denominator by $\sqrt 2$

${1 \over {a \pm \sqrt b }}$ its rationalization factor $a \mp \sqrt b$

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CBSE Class-9 Revision Notes and Key Points

Number Systems class 9 Notes. CBSE quick revision note for Class-9 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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