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Chapter 0: Problem 83

Can a real number be both rational and irrational? Explain your answer.

Short Answer

Expert verified
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.

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{x^{2}-12 x+36}{4 x-24} $$

Write each number in decimal notation. $$ 4.7 \times 10^{3} $$

simplify each algebraic expression. $$ 4(2 y-6)+3(5 y+10) $$

Write each number in decimal notation. $$ 7.86 \times 10^{-4} $$

state the name of the property illustrated. $$ 6 \cdot(2 \cdot 3)=6 \cdot(3 \cdot 2) $$
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