Real Numbers & Rationalization

Real Numbers & Rationalization. By Yash Raj Sidar.

Defining Real Numbers. Real Numbers. Real numbers include all the rational and irrational numbers, and they can be represented on the number line. They have the property of closure under addition, subtraction, multiplication, and division..

Rational Numbers. Representation. Rational numbers can be expressed as fractions, where the numerator and denominator are integers, and the denominator is not zero. They are also terminating or repeating decimals..

Irrational Numbers. Concept. Irrational numbers cannot be expressed as fractions, and their decimal forms are non-terminating and non-repeating. They are numbers that cannot be written as a simple fraction..

Rationalizing Denominators. Fraction Simplification.

Number Line Representation. Examples. Irrational numbers, such as the square root of 2 or π, are placed on the number line between rational numbers. Their placement reflects their non-repeating, non-terminating decimal representations..

Case Study: Real World Application. Example Problem.