How to examine irrational and rational numbers
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Answer:
A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.
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Step-by-step explanation:
Introduction of Irrational Numbers
An irrational number is a real number that cannot be expressed as a ratio of integers. example, √ 2. The real numbers which are not rational i.e. which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0 are known asirrational numbers. The decimal expansion of an irrational number is neither terminating nor recurring.
For Example √ 2, √ 3, √ pi, etc.
The above numbers are not a rational number as any number which can be represented in the form of p/q, such that, p and q are integers and q ≠ 0 is known as a rational number.
For Example, 2, 5/11, -5.12, 0.31 are all examples of rational numbers because the decimal expansion of an irrational number either terminates or repeats.
From the study of irrational numbers, if p is a prime number, then √ p is irrational. From this, it can be said that √ 2, √ 3, √ pi, etc. are all irrational numbers.