Math Problem Statement
Solution
The worksheet you're working on classifies numbers into different categories: Whole, Integer, Rational, and Irrational. Let's go through the numbers provided:
-
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
-
-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
-
√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.)
-
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
-
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
-
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:
- Why is every integer also a rational number?
- Can a rational number ever be irrational?
- What is the difference between rational and irrational numbers in terms of their decimal expansions?
- Are all square roots irrational?
- 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
-
Theorems
Properties of Number Systems
Suitable Grade Level
Grades 6-8
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