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Chapter 5: Problem 86

Describe the difference between a rational number and an irrational number.

Short Answer

Expert verified
Rational numbers can be expressed as a fraction or ratio of two integers, while irrational numbers cannot be written as such fractions. Decimal representations of irrational numbers neither terminate nor repeat.

Step by step solution

01

Define rational numbers

Rational numbers are any numbers that can be expressed as the quotient or fraction \( \frac{a}{b} \) of two integers, with the denominator \( b \) not equal to zero. The numbers 7, -3, -5.25, 2/3 are examples of rational numbers because each can be written as a fraction.
02

Define irrational numbers

Irrational numbers cannot be written as ratios or fractions. This includes numbers that do not terminate or do not repeat. \(\pi\), \(\sqrt{2}\), and the golden ratio (\(\phi\)) are examples of irrational numbers as these cannot be accurately expressed as a fraction.
03

Highlight the Difference

The key difference between rational and irrational numbers is that while rational numbers can be expressed as fractions (division of two integers), irrational numbers cannot. Irrational numbers, when written in decimal form, do not terminate nor repeat.

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