To determine which sets contain the number -1.576, let's analyze the characteristics of each set:
1. Natural Numbers:
- These are the set of positive integers starting from 1, 2, 3, and so on.
- -1.576 is not a positive integer.
- Conclusion: -1.576 is not a natural number.
2. Whole Numbers:
- These are the set of natural numbers including 0, i.e., 0, 1, 2, 3, and so on.
- -1.576 is not zero and also not a positive integer.
- Conclusion: -1.576 is not a whole number.
3. Integers:
- These include all positive and negative whole numbers, including zero.
- -1.576 has a fractional part and is not a whole number.
- Conclusion: -1.576 is not an integer.
4. Rational Numbers:
- These are numbers that can be expressed as the quotient or fraction [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex].
- -1.576 can be expressed as a fraction [tex]\(\frac{-1576}{1000}\)[/tex] when written in its fractional form.
- Conclusion: -1.576 is a rational number.
5. Irrational Numbers:
- These are numbers that cannot be expressed as a simple fraction, and their decimal representation is non-repeating and non-terminating.
- -1.576 has a terminating decimal representation.
- Conclusion: -1.576 is not an irrational number.
6. Real Numbers:
- These encompass both rational and irrational numbers.
- Since -1.576 is a rational number, it also falls into the category of real numbers.
- Conclusion: -1.576 is a real number.
Summary:
The number -1.576 belongs to the following sets:
- Rational numbers
- Real numbers
