Real Number Class 10 PPT Presentation Free Download

Real numbers include all numbers that can be represented on the number line. This category consists of both rational and irrational numbers. Real numbers are widely used in algebra, geometry, and real-life applications such as measurements and finance.

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Real Number Class 10 PPT Presentation Free Download

Types of Real Numbers

Real numbers can be classified into different categories:

1. Natural Numbers – These are counting numbers like 1, 2, 3, and so on.
2. Whole Numbers – These include all natural numbers along with zero.
3. Integers – These consist of all positive and negative whole numbers, including zero.
4. Rational Numbers – Any number that can be expressed as a fraction, where the numerator and denominator are integers and the denominator is not zero. Examples include fractions, decimals that terminate, and repeating decimals.
5. Irrational Numbers – Numbers that cannot be expressed as a fraction and have non-repeating, non-terminating decimal expansions. Examples include the square root of 2 and pi.

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Properties of Real Numbers

1. Closure Property – The sum, difference, and product of two real numbers is always a real number.
2. Commutative Property – Changing the order of numbers in addition or multiplication does not change the result.
3. Associative Property – The grouping of numbers in addition or multiplication does not affect the result.
4. Distributive Property – Multiplication distributes over addition, meaning a number multiplied by a sum is equal to the sum of individual multiplications.

Decimal Representation of Real Numbers

Real numbers can have different types of decimal expansions:

• Terminating Decimals – These end after a certain number of decimal places.
• Non-Terminating Repeating Decimals – These have a repeating pattern of digits.
• Non-Terminating Non-Repeating Decimals – These decimals go on forever without repeating and are always irrational numbers.

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Euclid’s Division Lemma and The Fundamental Theorem of Arithmetic

1. Euclid’s Division Lemma states that for any two numbers, one can be divided by the other to give a quotient and a remainder. This method is useful in finding the highest common factor (HCF).
2. The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of prime numbers. This is useful in prime factorization.

Table of Content for Real Number Class 10 PPT

• Definition
• Euclid’s Division Lemma And Algorithm
• Revisiting Rational numbers and their decimal expansions
• How to Check if a Number is Rational or Irrational?
• Irrational Numbers and Their Proofs
• Conclusion

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Real Number Class 10 PPT