Let's examine each of the different number sets to determine whether -2.22 belongs to them.
1. Natural Numbers:
- Natural numbers are the positive integers starting from 1 (i.e., 1, 2, 3, 4, ...).
- Since -2.22 is not a positive integer and is negative, it is not a natural number.
- Therefore, -2.22 is not in the set of natural numbers.
2. Whole Numbers:
- Whole numbers are non-negative integers (i.e., 0, 1, 2, 3, ...).
- Since -2.22 is negative and not an integer, it is not a whole number.
- Therefore, -2.22 is not in the set of whole numbers.
3. Integers:
- Integers include all positive and negative whole numbers, including zero (i.e., ..., -3, -2, -1, 0, 1, 2, 3, ...).
- Since -2.22 is not a whole number, it is not an integer.
- Therefore, -2.22 is not in the set of integers.
4. Rational Numbers:
- Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero (i.e., [tex]\( \frac{a}{b} \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are integers, and [tex]\( b \neq 0 \)[/tex]).
- Since -2.22 can be represented as -222/100, it is a rational number.
- Therefore, -2.22 is in the set of rational numbers.
5. Irrational Numbers:
- Irrational numbers cannot be expressed as a ratio of two integers. They have non-repeating, non-terminating decimal expansions (e.g., [tex]\( \pi \)[/tex], [tex]\( \sqrt{2} \)[/tex]).
- Since -2.22 can be expressed as a fraction, it is not an irrational number.
- Therefore, -2.22 is not in the set of irrational numbers.
6. Real Numbers:
- Real numbers include all rational and irrational numbers (essentially all numbers that can be found on the number line).
- Since -2.22 is a rational number, it is also a real number.
- Therefore, -2.22 is in the set of real numbers.
Summarizing, the sets that contain the number -2.22 are:
- Rational numbers
- Real numbers
