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Real Number

Real numbers are the combination of both rational and irrational numbers. They represent all possible values that can be plotted on a continuous number line, including integers, fractions, and non-terminating decimals.

Key Concepts

Real numbers encompass natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Every real number corresponds to a unique point on the number line, and every point on the number line represents a unique real number.

In the Class 10 curriculum, real numbers are studied to understand the Fundamental Theorem of Arithmetic and the properties of prime factorization.

Formula & Equation

HCF(a, b) x LCM(a, b) = a x b

a and b are two positive integers. HCF is the Highest Common Factor and LCM is the Least Common Multiple of these integers.

Common Misconceptions

Myth: All real numbers can be written as fractions.

Fact: Only rational numbers can be written as fractions in the form p/q. Irrational numbers, which are also real numbers, cannot be expressed as simple fractions.

Real World Applications

Measuring continuous physical quantities like distance, temperature, or time, where values can be exact integers or decimals like 5.4 kilometers.

Calculating the diagonal of a square room, which often results in an irrational real number such as the square root of 2.

Frequently Asked Questions

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction p/q where q is not zero. Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimal expansions.

Is zero considered a real number?

Yes, zero is a real number because it is a rational number that can be plotted exactly on the number line.

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