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In the context of number systems, which of the following statements best describ

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Question: In the context of number systems, which of the following statements best describes the relationship between rational and irrational numbers?

Options:

  1. Rational numbers can be expressed as fractions, while irrational numbers cannot.
  2. Irrational numbers can be expressed as fractions, while rational numbers cannot.
  3. Both rational and irrational numbers can be expressed as fractions.
  4. Rational numbers are always whole numbers.

Correct Answer: Rational numbers can be expressed as fractions, while irrational numbers cannot.

Solution: 

Rational numbers are defined as numbers that can be expressed as the quotient of two integers, while irrational numbers cannot be expressed in this way.

In the context of number systems, which of the following statements best describ

Practice Questions

Q1
In the context of number systems, which of the following statements best describes the relationship between rational and irrational numbers?
  1. Rational numbers can be expressed as fractions, while irrational numbers cannot.
  2. Irrational numbers can be expressed as fractions, while rational numbers cannot.
  3. Both rational and irrational numbers can be expressed as fractions.
  4. Rational numbers are always whole numbers.

Questions & Step-by-Step Solutions

In the context of number systems, which of the following statements best describes the relationship between rational and irrational numbers?
  • Step 1: Understand what rational numbers are. They are numbers that can be written as a fraction, where both the top number (numerator) and the bottom number (denominator) are whole numbers (integers).
  • Step 2: Recognize that irrational numbers are different. They cannot be written as a simple fraction. This means they cannot be expressed as a quotient of two integers.
  • Step 3: Examples of rational numbers include 1/2, 3, and -4. Examples of irrational numbers include √2, Ο€ (pi), and e (Euler's number).
  • Step 4: Conclude that the main difference is that rational numbers can be expressed as fractions, while irrational numbers cannot.
  • Rational Numbers – Numbers that can be expressed as the quotient of two integers.
  • Irrational Numbers – Numbers that cannot be expressed as the quotient of two integers.
  • Number Systems – The classification of numbers into rational and irrational categories.
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