Rational, Irrational, And Real Numbers

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MrsOswald

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Quizzes Created: 2 | Total Attempts: 10,803

Questions: 10 | Attempts: 1,376 | Updated: Mar 22, 2023

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Rational, Irrational, And Real Numbers - Quiz

Explore the distinctions between Rational, Irrational, and Real Numbers in this engaging quiz. Assess your understanding of number classifications, rationality, and the relationship between different types of numbers. Ideal for learners seeking to enhance their mathematical skills.

Questions and Answers

1.

Which of the following are Real numbers?
- A.
  
  6
- B.
  
  -17
- C.
  
  82.4
- D.
- E.
Correct Answer(s)
A. 6
B. -17
C. 82.4
D.
E.

Explanation
The numbers 6, -17, and 82.4 are all real numbers. Real numbers include all rational and irrational numbers, which means they can be expressed as a fraction or a decimal. In this case, 6 is a whole number, -17 is a negative whole number, and 82.4 is a decimal number. Therefore, all three numbers fall under the category of real numbers.

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1
2.

Which of the following are Rational numbers?
- A.
  
  93
- B.
  
  -12
- C.
  
  0
- D.
  
  -4.8
- E.
- F.
Correct Answer(s)
A. 93
B. -12
C. 0
D. -4.8

Explanation
All the given numbers are rational numbers. A rational number is any number that can be expressed as a fraction or a ratio of two integers. 93, -12, and 0 are all integers, and any integer can be expressed as a fraction by dividing it by 1. -4.8 can be expressed as the fraction -48/10, which can be simplified to -24/5. Therefore, all the given numbers can be expressed as fractions or ratios of integers, making them rational numbers.

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3
3.

Which of the following are Irrational numbers?
- A.
  
  3
- B.
- C.
- D.
  
  -92.56
- E.
Correct Answer
B.
4.

True for False: All Rational numbers are Real numbers.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
All rational numbers are real numbers because rational numbers can be expressed as fractions of two integers, and the set of real numbers includes all rational numbers along with irrational numbers. Rational numbers can be plotted on a number line and are part of the continuous number line that represents real numbers. Therefore, it is true that all rational numbers are real numbers.

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2
5.

True or False: All Real numbers are Rational numbers.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The statement "All Real numbers are Rational numbers" is false. While all rational numbers are real numbers, not all real numbers are rational. Real numbers include both rational numbers (which can be expressed as a fraction) and irrational numbers (which cannot be expressed as a fraction, such as √2 or π). Therefore, the statement is incorrect.

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1
6.

A number that can be written as a fraction is called a(n) _________ number.

Correct Answer
Rational
rational

Explanation
A number that can be written as a fraction is called a rational number. This includes both whole numbers and decimals that can be expressed as a ratio of two integers. The term "rational" refers to the fact that these numbers can be expressed as a ratio or fraction.

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2
7.

A number where the decimal never ends and never repreats is called a(n) _____________ number.

Correct Answer
Irrational
irrational

Explanation
An irrational number is a number where the decimal representation never ends and never repeats. This means that the digits after the decimal point go on forever without any pattern. Therefore, the given correct answer "Irrational" is appropriate in describing a number with these characteristics. The lowercase "irrational" is also correct as it refers to the same concept.

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8.

A number with a repeating decimal is a(n) ______________ number.

Correct Answer
Rational
rational
Real
real

Explanation
A number with a repeating decimal is called a rational number. Rational numbers can be expressed as a fraction, where the numerator and denominator are both integers. Repeating decimals can be written as fractions with repeating patterns. Therefore, a number with a repeating decimal is considered rational. Real numbers, on the other hand, include both rational and irrational numbers, so the statement "a number with a repeating decimal is a real number" is also true.

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9.

is which types of numbers? Check all that apply.
- A.
  
  Real
- B.
  
  Rational
- C.
  
  Irrational
Correct Answer(s)
A. Real
B. Rational

Explanation
Real numbers are a set of numbers that include all rational and irrational numbers. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Irrational numbers, on the other hand, cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. Therefore, the correct answer is Real and Rational, as all rational numbers are real numbers.

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1
10.

is which types of numbers? Check all that apply.
- A.
  
  Real
- B.
  
  Rational
- C.
  
  Irrational
Correct Answer(s)
A. Real
C. Irrational

Explanation
Real numbers are a set of numbers that include all rational and irrational numbers. Rational numbers are numbers that can be expressed as a fraction, while irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. Therefore, the answer "Real, Irrational" is correct because it includes both types of numbers.

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