Math Problem Statement

Classify numbers into the different number systems: Whole, Integer, Rational, and Irrational.

Solution

The worksheet you're working on classifies numbers into different categories: Whole, Integer, Rational, and Irrational. Let's go through the numbers provided:

  1. 0:

    • Whole: Yes (Whole numbers include 0 and all positive integers.)
    • Integer: Yes (Integers include negative numbers, zero, and positive numbers.)
    • Rational: Yes (0 can be expressed as 0/1, so it's rational.)
    • Irrational: No
  2. -7:

    • Whole: No (Whole numbers are non-negative.)
    • Integer: Yes (Negative whole numbers are integers.)
    • Rational: Yes (-7 can be expressed as -7/1.)
    • Irrational: No
  3. √13:

    • Whole: No (It’s not a non-negative integer.)
    • Integer: No (It’s not a whole number.)
    • Rational: No (√13 is not expressible as a fraction of integers.)
    • Irrational: Yes (Square roots of non-perfect squares are irrational.)
  4. 1.125:

    • Whole: No (It's not a non-negative integer.)
    • Integer: No (It’s a decimal, not an integer.)
    • Rational: Yes (1.125 can be expressed as 9/8.)
    • Irrational: No
  5. 0.3333... (repeating):

    • Whole: No (Not a non-negative integer.)
    • Integer: No (It's a repeating decimal.)
    • Rational: Yes (It’s a rational number since it equals 1/3.)
    • Irrational: No
  6. ¾:

    • Whole: No (It's a fraction.)
    • Integer: No (It’s not a whole number.)
    • Rational: Yes (It’s a rational number, as it’s a fraction.)
    • Irrational: No

Would you like more details on any of these classifications or corrections? Here are five questions to extend your understanding:

  1. Why is every integer also a rational number?
  2. Can a rational number ever be irrational?
  3. What is the difference between rational and irrational numbers in terms of their decimal expansions?
  4. Are all square roots irrational?
  5. Why is 0 considered a whole number?

Tip: Rational numbers can always be written as fractions, even if their decimal expansion is repeating or terminating.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Rational Numbers
Irrational Numbers
Integers
Whole Numbers

Formulas

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Theorems

Properties of Number Systems

Suitable Grade Level

Grades 6-8