Math Problem Statement
Classify each number as being a natural number (N), whole number (W), integer (I), rational number (Q), and/or irrational number (Q′).
ⓐ 36−−√
ⓑ 83
Solution
Let's classify each number according to the following categories:
- Natural Numbers (N): These are positive counting numbers: 1, 2, 3, etc.
- Whole Numbers (W): These include all natural numbers and zero: 0, 1, 2, 3, etc.
- Integers (I): These include all whole numbers and their negatives: ..., -2, -1, 0, 1, 2, etc.
- Rational Numbers (Q): These are numbers that can be expressed as a fraction , where and are integers, and .
- Irrational Numbers (Q′): These are numbers that cannot be expressed as a fraction of two integers (e.g., , ).
Now, let's classify the numbers:
ⓐ
- Natural Number (N): Yes, 6 is a natural number.
- Whole Number (W): Yes, 6 is a whole number.
- Integer (I): Yes, 6 is an integer.
- Rational Number (Q): Yes, 6 can be expressed as , so it's rational.
- Irrational Number (Q′): No, is not irrational because it simplifies to a rational number (6).
So, is a natural number, whole number, integer, and rational number.
ⓑ 83
- 83 is a positive integer.
- Natural Number (N): Yes, 83 is a natural number.
- Whole Number (W): Yes, 83 is a whole number.
- Integer (I): Yes, 83 is an integer.
- Rational Number (Q): Yes, 83 can be expressed as , so it's rational.
- Irrational Number (Q′): No, 83 is not irrational.
So, 83 is a natural number, whole number, integer, and rational number.
Summary:
- ⓐ : N, W, I, Q
- ⓑ 83: N, W, I, Q
Would you like more details or have any questions?
Here are 5 related questions:
- Can an irrational number also be a rational number?
- Is a rational or irrational number?
- How do you determine if a square root is rational or irrational?
- Is zero considered a natural number or just a whole number?
- What is the smallest positive integer?
Tip: A square root of a perfect square is always a rational number.
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Math Problem Analysis
Mathematical Concepts
Number Classification
Square Roots
Rational and Irrational Numbers
Formulas
√n for square roots
Fraction form for rational numbers (a/b where b ≠ 0)
Theorems
The square root of a perfect square is a rational number
A number is rational if it can be written as a fraction of two integers
Suitable Grade Level
Grades 6-8
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