Choose all the sets containing the number –1.576.
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
The set containing the number -1.576 is:
- Integers
- Rational numbers
- Irrational numbers
- Real numbers
To determine which sets contain the number -1.576, let's understand each of these sets:
1. Natural numbers: The set of natural numbers includes all positive integers starting from 1. Natural numbers do not include negative numbers or fractions. Therefore, -1.576 is not included in the set of natural numbers.
2. Whole numbers: The set of whole numbers includes all natural numbers along with zero. Similar to natural numbers, whole numbers do not include negative numbers or fractions. Therefore, -1.576 is not included in the set of whole numbers.
3. Integers: The set of integers includes positive and negative whole numbers, along with zero. It includes both positive and negative values. Therefore, -1.576 is included in the set of integers.
4. Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where both the numerator and denominator are integers. Rational numbers include both integers and fractions. Therefore, -1.576 can be expressed as -1576/1000 or -187/119, making it a rational number.
5. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction. They are non-repeating, non-terminating decimals. -1.576 can be expressed as a decimal, and it terminates after the thousandth place. Therefore, -1.576 is not categorized as an irrational number.
6. Real numbers: Real numbers include all rational and irrational numbers. Since -1.576 is a rational number, it is also a real number.
In conclusion, the sets that contain the number -1.576 are:
- Integers
- Rational numbers
- Real numbers