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We will work on your suggestions as soon as possible. Your support is what keeps us going. Class IX Mathematics Notes. Contains solved exercises, review questions, MCQs, important board questions and chapter overview. Unit 2 - Real and Complex Numbers Exercise 2. Unit 3 - Logarithms Exercise 3. Unit 5 - Factorization Exercise 5. Unit 10 - Congruent Triangles Theorem Unit 11 - Parallelograms and Triangles Theorem Unit 13 - Sides and Angles of Triangles Theorem Byjus Class 10 Maths Notes Ltd Unit 15 - Pythagoras' Theorem Theorem Unit 17 - Practical Geometry Triangles Exercise Glossary Glossary.

The remainder never becomes zero In this case, we have a repeating block of digits in the quotient, this expansion is called non-terminating recurring. Note: The decimal expansion of rational number is either terminating or non-terminating recurring. Moreover, a number whose decimal expansion is terminating or non-terminating recurring is rational. The Byjus Class 6 Maths Notes Game decimal expansion of an irrational number is non-terminating non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is irrational.

Operations on Real Numbers: Rational numbers satisfy the commutative, associative and distributive laws for addition and multiplication. Moreover, if we add, subtract, multiply or divide except by zero two rational numbers. We still get a rational number i. Irrational numbers also satisfy the commutative, associated and distributive laws for addition and multiplication.

However, the sum, difference, quotients and products of irrational numbers are not always. Note: The sum or difference of a rational number and an irrational number is irrational. The product or quotient of a non-zero rational number with an irrational number is irrational. If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational. Rationalising the Denominator: When the denominator of an expression contains a term with a square root or a number under a radical sign , the process of converting it to an equivalent expression whose denominator is a rational number is called rationalising the denominator.

Here a, b, n and m are natural numbers. Here, a is called base and m and n are the exponents. Laws of Radicals: Let a and b be positive real numbers. Laws of Exponents a m.

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