A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it can be written as a fraction. Examples of rational numbers include 1/2, -3/4, 5, and -8.
On the other hand, an irrational number cannot be expressed as a simple fraction and has an infinite number of non-repeating decimal places. These decimals go on forever without exhibiting any pattern. Examples of irrational numbers include √2, π (pi), and e.
To determine if a given number is rational or irrational, you can follow these steps:
1. Representation: Check if the number is expressed as a simple fraction or an exact radical (√n). If it is, then it is a rational number. For example, 3/4 and √9 = 3 are rational numbers.
2. Decimal representation: If the number cannot be expressed as a fraction or a simple radical, examine its decimal representation. If the decimal terminates or repeats, then it is a rational number. For example, 0.75 and 0.3333... are rational numbers.
3. Nonterminating, non-repeating decimals: If the decimal representation of the number goes on forever without repeating any pattern, it is an irrational number. For example, the decimal representation of √2 = 1.41421356... does not terminate or repeat.
In summary, rational numbers can be written as fractions or terminate/repeat as decimals, while irrational numbers cannot be expressed as simple fractions and have non-repeating, non-terminating decimal representations.
Explain how you can tell the difference between a rational number and an irrational number.
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