To determine which sets contain the number -1.576, let's analyze each set step-by-step:
1. Natural Numbers: Natural numbers are the set of positive integers starting from 1 (1, 2, 3, ...). Negative numbers and numbers with fractional parts are not included in this set. Thus, -1.576 is not a natural number.
- Result: Not in the set of natural numbers.
2. Whole Numbers: Whole numbers are the set of non-negative integers starting from 0 (0, 1, 2, 3, ...). Again, negative numbers and numbers with fractional parts are not included. Therefore, -1.576 is not a whole number.
- Result: Not in the set of whole numbers.
3. Integers: Integers include all positive and negative whole numbers, including zero (..., -2, -1, 0, 1, 2, ...). Numbers with fractional or decimal parts are not included. Thus, -1.576 is not an integer.
- Result: Not in the set of integers.
4. Rational Numbers: Rational numbers are numbers that can be expressed as the ratio of two integers (i.e., fractions). Since -1.576 can be written as -1576/1000, it is a rational number.
- Result: In the set of rational numbers.
5. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a ratio of two integers. Since -1.576 can be expressed as a ratio of two integers, it is not an irrational number.
- Result: Not in the set of irrational numbers.
6. Real Numbers: Real numbers include all rational and irrational numbers. Since -1.576 is identified as a rational number, it is definitely a real number.
- Result: In the set of real numbers.
In conclusion:
- The number -1.576 belongs to the set of rational numbers.
- The number -1.576 belongs to the set of real numbers.
Therefore, the sets containing the number -1.576 are:
- Rational numbers
- Real numbers
