Math Problem Statement

Classify each number by naming all the subsets in which it is an element.

Solution

Let's analyze and classify each number into its correct subsets based on the provided options:

Subsets Legend:

  • A: Real, Irrational
  • B: Real, Rational
  • C: Real, Rational, Integer
  • D: Real, Rational, Integer, Whole
  • E: Real, Rational, Integer, Whole, Natural

Numbers to Classify:

  1. -4:

    • It's a real number.
    • It's a rational number (since it can be expressed as -4/1).
    • It's an integer.
    • It's not a whole number (since whole numbers are non-negative).
    • Correct classification: C.
  2. 6.5:

    • It's a real number.
    • It's a rational number (as 6.5 can be expressed as 13/2).
    • It's not an integer or whole number.
    • Correct classification: B.
  3. √5:

    • It's a real number.
    • It's an irrational number (since √5 cannot be expressed as a fraction).
    • Correct classification: A.
  4. :

    • It's a real number.
    • It's a rational number (⅔ is a fraction of two integers).
    • It's not an integer.
    • Correct classification: B.
  5. 1.390864... (non-repeating decimal):

    • It's a real number.
    • It's an irrational number (since it doesn't repeat and can't be expressed as a fraction).
    • Correct classification: A.
  6. −√9:

    • It's a real number.
    • √9 = 3, so −√9 = -3.
    • It's a rational number (as -3 can be expressed as -3/1).
    • It's an integer.
    • Correct classification: C.

Now let's summarize the answers:

  1. -4C
  2. 6.5B
  3. √5A
  4. B
  5. 1.390864...A
  6. −√9C

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

  1. What is the difference between rational and irrational numbers?
  2. Can irrational numbers ever be represented as fractions?
  3. What defines a whole number versus an integer?
  4. How are real numbers classified in mathematical sets?
  5. Can the square root of any number be rational?

Tip: Rational numbers are always expressible as fractions, while irrational numbers have non-terminating, non-repeating decimals.

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Math Problem Analysis

Mathematical Concepts

Number classification
Real numbers
Rational and Irrational numbers

Formulas

-

Theorems

Classification of numbers into sets

Suitable Grade Level

Grades 6-9