To classify the number -1.576 into the appropriate sets of real numbers, let's break down each category and determine whether the number -1.576 belongs to that set.
1. Natural Numbers:
Natural numbers are positive integers starting from 1 (i.e., 1, 2, 3, etc.). They do not include zero, negative numbers, or any decimal numbers.
- Since -1.576 is negative and not an integer, it is not a natural number.
2. Whole Numbers:
Whole numbers include all natural numbers along with zero (i.e., 0, 1, 2, 3, etc.). Again, they do not include negative numbers or decimals.
- Since -1.576 is negative and not an integer, it is not a whole number.
3. Integers:
Integers consist of all whole numbers and their negative counterparts (i.e., ..., -3, -2, -1, 0, 1, 2, 3, ...).
- Since -1.576 has a decimal part, it is not an integer.
4. Rational Numbers:
Rational numbers can be expressed as the ratio of two integers (i.e., in the form [tex]\( \frac{a}{b} \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are integers and [tex]\( b \neq 0 \)[/tex]). This includes all integers as well as fractions and terminating or repeating decimals.
- Since -1.576 can be written as the fraction [tex]\( \frac{-1576}{1000} \)[/tex], it is a rational number.
5. Irrational Numbers:
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They have non-terminating, non-repeating decimal expansions (e.g., [tex]\( \pi \)[/tex], [tex]\( \sqrt{2} \)[/tex], etc.).
- Since -1.576 is a rational number, it is not an irrational number.
6. Real Numbers:
Real numbers include all rational and irrational numbers. In other words, any number that can be placed on the number line.
- Since -1.576 is a rational number, it is also a real number.
Based on this analysis, the number -1.576 belongs to the following sets:
- Rational Numbers
- Real Numbers
