Spectrum Math Grade 8 Chapter 2 Lesson 1 Answer Key Understanding Rational and Irrational Numbers

Students can use the Spectrum Math Grade 8 Answer Key Chapter 2 Lesson 2.1 Understanding Rational and Irrational Numbers as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 2 Lesson 2.1 Understanding Rational and Irrational Numbers Answers Key

A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Here are some examples of rational numbers: 3, -5, \(\frac{1}{3}\), \(4 . \overline{66}\), \(\frac{5}{11}\), 3.25
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Here are some examples of irrational numbers: 5.23143.,.,, π

Tell if each number is rational or irrational.

Question 1.
a. \(\frac{1}{5}\)
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, \(\frac{1}{5}\) is a rational number

b. \(\sqrt{5}\)
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Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, \(\sqrt{5}\) is an irrational number

c. -5
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, -5 is a rational number

Question 2.
a.

Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

b. \(\frac{1}{3}\)
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, \(\frac{1}{3}\) is a rational number

c.
2.345
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, 2.345 is a rational number

Question 3.
a.

Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

b. \(3 . \overline{45}\)
Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, \(3 . \overline{45}\) is a rational number

c. \(\frac{7}{9}\)
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, \(\frac{7}{9}\) is a rational number

Question 4.
a.

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Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

b. 19.294153
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Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

c. –\(\frac{4}{5}\)
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, –\(\frac{4}{5}\) is a rational number

Question 5.
a.
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Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

b. π
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Answer: Irrational number
An irrational number is any decimal that does not terminate and never repeats. These numbers are often represented by symbols.
Therefore, the given number is an irrational number

c. –\(\frac{7}{10}\)
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Answer: Rational number
A rational number is a number that either terminates or repeats a pattern. It can be written as a fraction, \(\frac{a}{b}\), where a and b are both whole number integers and b does not equal zero.
Therefore, –\(\frac{7}{10}\) is a rational number