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Which of the following is a characteristic of irrational numbers?

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Question: Which of the following is a characteristic of irrational numbers?

Options:

  1. They can be expressed as a fraction.
  2. They have a non-repeating, non-terminating decimal expansion.
  3. They are always positive.
  4. They can be represented on a number line as whole numbers.

Correct Answer: They have a non-repeating, non-terminating decimal expansion.

Solution: 

Irrational numbers are characterized by their non-repeating, non-terminating decimal expansion, distinguishing them from rational numbers.

Which of the following is a characteristic of irrational numbers?

Practice Questions

Q1
Which of the following is a characteristic of irrational numbers?
  1. They can be expressed as a fraction.
  2. They have a non-repeating, non-terminating decimal expansion.
  3. They are always positive.
  4. They can be represented on a number line as whole numbers.

Questions & Step-by-Step Solutions

Which of the following is a characteristic of irrational numbers?
  • Step 1: Understand what irrational numbers are. They are numbers that cannot be expressed as a simple fraction.
  • Step 2: Learn about decimal expansions. A decimal expansion is how we write numbers using a decimal point.
  • Step 3: Identify the key feature of irrational numbers: their decimal expansion goes on forever without repeating.
  • Step 4: Compare this with rational numbers, which can be written as fractions and have decimal expansions that either terminate (end) or repeat.
  • Step 5: Conclude that the main characteristic of irrational numbers is their non-repeating, non-terminating decimal expansion.
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