Rational and irrational numbers are two distinct subsets of real numbers.
Rational numbers can be expressed as the ratio of two integers, where the denominator is not zero. For example, 1/2, 3/4, and -5/7 are all rational numbers. Rational numbers can be expressed either as terminating decimals (such as 0.25) or as repeating decimals (such as 0.333... for 1/3).
Irrational numbers, on the other hand, cannot be expressed as a simple fraction or a ratio of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include π (pi), √2 (the square root of 2), and e (Euler's number).
Despite being distinct, rational and irrational numbers are related in that together they make up the entire set of real numbers. In other words, any real number can be classified as either rational or irrational. This relationship can be demonstrated by the fact that the sum, difference, product, and quotient of a rational number and an irrational number can result in an irrational number. For example, √2 + 1 is an irrational number, and 3/4 * π is also an irrational number.
In summary, while rational and irrational numbers are distinct subsets of real numbers, they are related because together they form the entirety of the real number system.
How are rational and irrational numbers related
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