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Question: What is the difference between a rational and irrational number?
Answer: In mathematics, numbers are classified into different categories based on their properties and characteristics
Question: What is the difference between a rational and irrational number?
Answer: In mathematics, numbers are classified into different categories based on their properties and characteristics. Two fundamental categories of numbers are rational and irrational numbers.
1. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction, where both the numerator and denominator are integers. The word “rational” is derived from “ratio,” emphasizing the idea of a relationship between two quantities. Rational numbers can be positive or negative.
Examples of rational numbers include:
– Integers: -3, 0, 5
– Fractions: 1/2, -4/7, 3/5
– Decimals that can be expressed as fractions: 0.25 (1/4), 1.6 (8/5)
Rational numbers can be finite (terminating decimal) or infinite (repeating decimal). For example, 0.333… (1/3) is an infinite repeating decimal.
2. Irrational Numbers: Irrational numbers cannot be expressed as a fraction of two integers. They cannot be written as terminating or repeating decimals. The decimal representation of an irrational number goes on indefinitely without repeating. The name “irrational” comes from the word “ratio,” with the prefix “ir-” meaning “not” or “non-.”
Examples of irrational numbers include:
– Square roots of non-perfect square numbers: √2, √5, √7
– π (pi), the ratio of a circle’s circumference to its diameter: 3.14159…
– e, the base of the natural logarithm: 2.71828…
– √3, √6, and all other non-perfect square roots
Irrational numbers are infinite and non-repeating. They cannot be represented as a fraction or ratio. Their decimal representation is non-terminating and non-repeating, making them non-repetitive patterns.
In summary, rational numbers can be expressed as fractions or terminating/repeating decimals, while irrational numbers cannot be expressed as fractions and have non-repeating non-terminating decimal representations.
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