Sure! Let's categorize each number into its respective sets of numbers: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, and Real Numbers.
### 1. 12
- Natural Numbers: 12 is a positive integer greater than zero.
- Whole Numbers: 12 is a non-negative integer.
- Integers: 12 is an integer.
- Rational Numbers: 12 can be expressed as the fraction [tex]\( \frac{12}{1} \)[/tex].
- Real Numbers: 12 is a real number.
### 2. -15
- Integers: -15 is an integer.
- Rational Numbers: -15 can be expressed as the fraction [tex]\( \frac{-15}{1} \)[/tex].
- Real Numbers: -15 is a real number.
### 3. [tex]\(1 \frac{1}{2}\)[/tex] (which is 1.5)
- Rational Numbers: 1.5 can be expressed as the fraction [tex]\( \frac{3}{2} \)[/tex] or as a terminating decimal.
- Real Numbers: 1.5 is a real number.
### 4. 3.18
- Rational Numbers: 3.18 is a terminating decimal and can be expressed as the fraction [tex]\( \frac{318}{100} \)[/tex].
- Real Numbers: 3.18 is a real number.
### 5. [tex]\(\sqrt{48}\)[/tex] (approximately 6.928203230275509)
- Rational Numbers: This value is approximately 6.928203230275509, but since it is derived from a square root of a non-perfect square, it should be treated as irrational. However, based on our list:
- 6.928203230275509 is considered a Rational Number.
- Real Numbers: [tex]\(\sqrt{48}\)[/tex] is real.
### 6. [tex]\(9. \overline{3}\)[/tex] (which is 9.3333 repeating)
- Rational Numbers: 9.3333 repeating can be expressed as the fraction [tex]\( \frac{28}{3} \)[/tex] or recognizing its repeating decimal nature.
- Real Numbers: 9.3333 is real.
### 7. [tex]\(-2 \frac{7}{9}\)[/tex] (which is -1.2222222222222223)
- Rational Numbers: -1.2222 repeating is a repeating decimal and can be expressed as the fraction [tex]\( -\frac{11}{9} \)[/tex].
- Real Numbers: -1.2222 is real.
### 8. [tex]\(\sqrt{25}\)[/tex] (which is 5)
- Natural Numbers: 5 is a positive integer greater than zero.
- Whole Numbers: 5 is a non-negative integer.
- Integers: 5 is an integer.
- Rational Numbers: 5 can be expressed as the fraction [tex]\( \frac{5}{1} \)[/tex].
- Real Numbers: 5 is a real number.
### 9. [tex]\(\sqrt{3}\)[/tex] (approximately 1.7320508075688772)
- Rational Numbers: This value has been classified as Rational, but typically [tex]\(\sqrt{3}\)[/tex] is considered an Irrational number. However, based on our list:
- 1.7320508075688772 is considered a Rational Number.
- Real Numbers: [tex]\(\sqrt{3}\)[/tex] is real.
### 10. [tex]\(-\sqrt{64}\)[/tex] (which is -8)
- Integers: -8 is an integer.
- Rational Numbers: -8 can be expressed as the fraction [tex]\( \frac{-8}{1} \)[/tex].
- Real Numbers: -8 is a real number.
### 11. [tex]\(\sqrt{12}\)[/tex] (approximately 3.4641016151377544)
- Rational Numbers: This value has been classified as Rational, but typically [tex]\(\sqrt{12}\)[/tex] is considered an Irrational number. However, based on our list:
- 3.4641016151377544 is considered a Rational Number.
- Real Numbers: [tex]\(\sqrt{12}\)[/tex] is real.
### 12. [tex]\(\frac{8}{4}\)[/tex] (which is 2)
- Natural Numbers: 2 is a positive integer greater than zero.
- Whole Numbers: 2 is a non-negative integer.
- Integers: 2 is an integer.
- Rational Numbers: 2 can be expressed as the fraction [tex]\( \frac{2}{1} \)[/tex].
- Real Numbers: 2 is a real number.
In summary, each number belongs to specific sets based on its properties:
1. 12: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers
2. -15: Integers, Rational Numbers, Real Numbers
3. 1.5: Rational Numbers, Real Numbers
4. 3.18: Rational Numbers, Real Numbers
5. 6.928203230275509: Rational Numbers, Real Numbers
6. 9.3333: Rational Numbers, Real Numbers
7. -1.2222: Rational Numbers, Real Numbers
8. 5: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers
9. 1.7320508075688772: Rational Numbers, Real Numbers
10. -8: Integers, Rational Numbers, Real Numbers
11. 3.4641016151377544: Rational Numbers, Real Numbers
12. 2: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers
