Math Problem Statement

Classify each number below as a rational number or an irrational number.

Solution

Let's classify the numbers from the table as either rational or irrational:

  1. −18π:

    • π (pi) is an irrational number because it cannot be expressed as a fraction of two integers.
    • −18π is the product of an irrational number (π) and a rational number (−18), which results in an irrational number.
  2. −2√3:

    • √3 (square root of 3) is irrational because it is not a perfect square and cannot be expressed as a fraction.
    • −2√3 is the product of a rational number (−2) and an irrational number (√3), which results in an irrational number.
  3. −92.45:

    • This is a terminating decimal, which can be expressed as a fraction (−9245/100), meaning it is a rational number.
  4. √49:

    • √49 (square root of 49) is a perfect square, equal to 7, which is a rational number.
    • So, √49 is a rational number.
  5. −70.49:

    • This is a terminating decimal, which can be expressed as a fraction (−7049/100), meaning it is a rational number.

Final classification:

  • −18π → irrational
  • −2√3 → irrational
  • −92.45 → rational
  • √49 → rational
  • −70.49 → rational

Would you like any further details or explanations?

Here are 5 related questions you might want to consider:

  1. What is the difference between rational and irrational numbers?
  2. How do you prove that a number like π is irrational?
  3. Are all square roots irrational?
  4. How can you express a terminating decimal as a fraction?
  5. What happens when you multiply a rational number by an irrational number?

Tip: Remember, any terminating or repeating decimal is always rational because it can be expressed as a fraction!

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Math Problem Analysis

Mathematical Concepts

Rational Numbers
Irrational Numbers
Decimals
Square Roots

Formulas

A rational number is any number that can be expressed as a fraction.
An irrational number is a number that cannot be expressed as a fraction.

Theorems

A terminating decimal is a rational number.
The product of a rational and an irrational number is irrational.
Perfect squares have rational square roots.

Suitable Grade Level

Grades 7-9