Problem 83
Question
Can a real number be both rational and irrational? Explain your answer.
Step-by-Step Solution
Verified Answer
No, a real number can't be both rational and irrational. This is because by definition, a rational number can be expressed as the fraction of two integers, while an irrational number can't.
1Step 1: Understand the definition of a Rational number
A Rational number is any number that can be expressed as the fraction \(a/b\), where \(a\) and \(b\) are integers and \(b\) not equal to 0.
2Step 2: Understand the definition of an Irrational number
An Irrational number cannot be expressed as the fraction of two integers. This means its decimal representation is neither terminating nor repeating.
3Step 3: Determine if a number can be both Rational and Irrational
Considering the definitions of rational and irrational numbers, it's evident that a number can't be both. If it can be expressed as a fraction, it's rational. If not, it's irrational. There is no overlap between these definitions.
Other exercises in this chapter
Problem 83
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