Tell which set or sets the number below belongs​ to: natural​ numbers, whole​ numbers, integers, rational​ numbers, irrational​ numbers, or real numbers.
negative 8
Question content area bottom
Part 1
Select all sets in which the number negative 8 is an element.
A.
irrational numbers
B.
whole numbers
C.
natural numbers
D.
rational numbers
E.
real numbers
F.
integers

To determine which set or sets the number \(-8\) belongs to, let's review each of the number sets mentioned:

1. **Natural Numbers:** These are the counting numbers starting from \(1\), \(2\), \(3\), and so on. Natural numbers do not include zero or any negative numbers. Therefore, \(-8\) is **not** a natural number.

2. **Whole Numbers:** This set includes all natural numbers plus zero, so it starts from \(0\), \(1\), \(2\), \(3\), and so on. Whole numbers do not include negative numbers. Therefore, \(-8\) is **not** a whole number.

3. **Integers:** Integers include all whole numbers as well as their negative counterparts, such as \(-3\), \(-2\), \(-1\), \(0\), \(1\), \(2\), \(3\), etc. Since \(-8\) is a negative whole number, it is an integer. So, \(-8\) **is** an integer.

4. **Rational Numbers:** Rational numbers are numbers that can be expressed as the quotient or fraction of two integers (where the denominator is not zero). \(-8\) can be written as \(-8/1\), which is a fraction of two integers. Hence, \(-8\) **is** a rational number.

5. **Irrational Numbers:** These are numbers that cannot be expressed as a simple fraction of two integers. They include numbers like \(\pi\) and \(\sqrt{2}\). Since \(-8\) can be expressed as a fraction, it is not an irrational number. Therefore, \(-8\) is **not** an irrational number.

6. **Real Numbers:** This set includes all rational and irrational numbers. Since \(-8\) is a rational number, it is also a real number. Hence, \(-8\) **is** a real number.

### Conclusion:
\(-8\) belongs to the following sets:
- Integers (F)
- Rational numbers (D)
- Real numbers (E)

\(-8\) does not belong to:
- Irrational numbers (A)
- Whole numbers (B)
- Natural numbers (C)

**Would you like more details or have any questions?**

### Here are 5 related questions for further exploration:
1. What sets do the number \(0\) belong to?
2. Is \(0.333...\) (repeating) a rational or an irrational number?
3. Can all integers be considered real numbers?
4. What is the difference between rational and irrational numbers?
5. How are natural numbers and whole numbers related?

**Tip:** Remember, integers include both positive and negative whole numbers, but not fractions or decimals that aren't whole.

Explore which mathematical sets the number negative 8 belongs to, including integers, rational numbers, and real numbers. Learn the definitions and properties of these sets with clear explanations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation