NCERT Class 9 Maths Chapter 3 The World of Numbers Notes

CBSE class 9 Maths Chapter 3 The World of Numbers is very interesting chapter. Math can be nightmare for some students as it contains complex formula, diagram and involves critical thinking. But some students also enjoy solving complex math problem.

In The World of Numbers Notes students will learn about the fundamental concepts of rational numbers, irrational numbers, real numbers, decimal forms of real numbers and their representation on the number line. These concepts will strength the concept and prepare students for upcoming exam.

The World of Numbers Notes

NCERT Class 9 Maths Chapter 3 Notes - Page 1
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Important Topics

For any positive real number (x), we have:

[x=(x+12)2−(x+12)2][ x = \left(\frac{x+1}{2}\right)^2 – \left(\frac{x+1}{2}\right)^2 ]

For real numbers (a > 0) and (b > 0):

i.(ab=a×b)i. (\sqrt{ab} = \sqrt{a} \times \sqrt{b})
ii.(ab=ab)ii. (\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}})
iii.(a+b)(a−b)=a−biii. (\sqrt{a} + \sqrt{b})(\sqrt{a} – \sqrt{b}) = a – b
iv.(a+b)(c+d)=ac+bc+ad−bdiv. (\sqrt{a} + \sqrt{b})(\sqrt{c} + \sqrt{d}) = \sqrt{ac} + \sqrt{bc} + \sqrt{ad} – \sqrt{bd}
v.(a+b)(a−b)=a2−bv. (a + \sqrt{b})(a – \sqrt{b}) = a^2 – b
vi.(a+b)2=a+b+2abvi. (\sqrt{a} + \sqrt{b})^2 = a + b + 2\sqrt{ab}

All-natural numbers, whole numbers and integer are rational number.

Equivalent rational numbers (or fractions) have same (equal) values when written in the simplest form.

Rational number between two numbers x and y

y=x+y2y = \dfrac{x+y}{2}

There are infinitely many rational numbers between any two given rational numbers.

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