What are real numbers?

Real numbers include both rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi). Any number that can be placed on a number line is a real number.

What is the Fundamental Theorem of Arithmetic?

The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of prime numbers, and this factorisation is unique, apart from the order in which the prime factors occur.

What is the relationship between HCF and LCM of two numbers?

For any two positive integers a and b, the product of their HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is equal to the product of the two numbers. That is, HCF(a, b) × LCM(a, b) = a × b.

How do we identify an irrational number?

An irrational number cannot be expressed as a simple fraction (p/q). In decimal form, it is non-terminating and non-repeating. Examples include square roots of non-perfect squares.

How to find if a rational number has a terminating decimal expansion?

A rational number in its simplest form (p/q) has a terminating decimal expansion if the prime factorisation of its denominator (q) is of the form 2^n × 5^m, where n and m are non-negative integers.

What are real numbers?

Real numbers include both rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi). Any number that can be placed on a number line is a real number.

What is the Fundamental Theorem of Arithmetic?

The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of prime numbers, and this factorisation is unique, apart from the order in which the prime factors occur.

What is the relationship between HCF and LCM of two numbers?

For any two positive integers a and b, the product of their HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is equal to the product of the two numbers. That is, HCF(a, b) × LCM(a, b) = a × b.

How do we identify an irrational number?

An irrational number cannot be expressed as a simple fraction (p/q). In decimal form, it is non-terminating and non-repeating. Examples include square roots of non-perfect squares.

How to find if a rational number has a terminating decimal expansion?

A rational number in its simplest form (p/q) has a terminating decimal expansion if the prime factorisation of its denominator (q) is of the form 2^n × 5^m, where n and m are non-negative integers.

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