Real numbers, as defined in class 10 mathematics, are essentially any number that can be represented on a number line.
That means a real number encompasses all rational and irrational numbers. Let's break this down:
- Rational Numbers: These can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. Examples include 1/2, -3/4, 5 (which is 5/1), and 0.
- Irrational Numbers: These cannot be expressed as a simple fraction. Their decimal representations are non-terminating and non-repeating. Famous examples include π (pi) and √2 (the square root of 2).
Therefore, the set of real numbers (denoted by the symbol "R") includes:
- Natural Numbers: (1, 2, 3, ...)
- Whole Numbers: (0, 1, 2, 3, ...)
- Integers: (... -3, -2, -1, 0, 1, 2, 3, ...)
- Rational Numbers: (numbers expressible as p/q, where p and q are integers and q ≠ 0)
- Irrational Numbers: (numbers that cannot be expressed as p/q)
In simpler terms, if you can plot a number on a number line, it's a real number. Real numbers can be positive, negative, or zero. They can be integers, fractions, or decimals (terminating or non-terminating and repeating or non-repeating).
