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Real numbers include all the numbers that we can locate on the number line. They encompass both rational and irrational numbers. Rational numbers can be expressed as a fraction where both the numerator and denominator are integers. For example:
• 1/2
• 3/4
Irrational numbers, on the other hand, cannot be expressed as such fractions. They don't terminate or repeat in their decimal form. All these types together make up the real number system, which forms the foundation of most of mathematics. Without real numbers, calculations in both simple arithmetic and more complex algebra would not be possible.

Fractions are a way to represent any number as the ratio of two integers. They are written in the form \( \frac{a}{b} \) where 'a' is the numerator, and 'b' is the denominator. Fractions are versatile and can describe quantities between whole numbers. For instance, the fraction \( \frac{3}{5} \) can represent three parts out of five equal parts. Understanding fractions is crucial because they help us understand how numbers can be divided and combined. They also provide a good basis for understanding more complex mathematical concepts like ratios, proportions, and rational numbers.

Irrational numbers are unique because they cannot be expressed as simple fractions. They are an essential part of the real number system and have several interesting properties. Some famous examples include:
• \(\pi\) : This is the ratio of the circumference of a circle to its diameter. It is approximately 3.14159 but continues indefinitely without repeating.
• \(e\) : Known as Euler's number, it is the base of natural logarithms and is approximately 2.71828.
• \(\text{√2}\): The square root of 2 which is approximately 1.414213. It is the length of the diagonal of a square with side length 1.
Understanding irrational numbers can help in various fields like engineering, physics, and computer science. Recognizing that not all numbers can be neatly expressed as fractions adds depth to our understanding of mathematics.