Math Problem Statement

Which of the following are irrational numbers?

Solution

The question asks, "Which of the following are irrational numbers?"

Let's analyze the options:

  1. π (pi): This is an irrational number because it cannot be expressed as a simple fraction. Its decimal expansion is non-repeating and infinite.
  2. 9.69̅ (repeating 9.69): This is a rational number. A repeating decimal can be converted into a fraction, so it is not irrational.
  3. 4: This is a whole number, which can be written as a fraction (4/1), making it a rational number.
  4. 0: This is a rational number, as it can be expressed as the fraction 0/1.

Thus, the only irrational number in this list is π.

Would you like more details, or have any other questions?

Here are 5 related questions to expand your understanding:

  1. What makes a number irrational?
  2. Can the square root of any number be irrational?
  3. Are there other famous irrational numbers like π?
  4. What is the difference between rational and irrational numbers in terms of decimals?
  5. How can repeating decimals always be converted to fractions?

Tip: A repeating decimal is always a rational number because it can be written as a ratio of two integers.

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Math Problem Analysis

Mathematical Concepts

Irrational Numbers
Rational Numbers

Formulas

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Theorems

Irrational numbers cannot be expressed as a ratio of two integers
Repeating decimals are rational

Suitable Grade Level

Grades 6-8