Certainly! Let's classify the number -2.22 by determining which sets it belongs to one by one.
1. Natural Numbers:
- Natural numbers are the set of positive integers starting from 1 and going upwards like 1, 2, 3, and so forth.
- Since -2.22 is a negative number and not a positive integer, it is not a natural number.
- Answer: False
2. Whole Numbers:
- Whole numbers include all the natural numbers and zero. Hence, the set starts from 0 and includes 1, 2, 3, etc.
- -2.22 is negative and not zero or a positive integer.
- Therefore, -2.22 is not a whole number.
- Answer: False
3. Integers:
- Integers include all whole numbers and their negative counterparts like ..., -3, -2, -1, 0, 1, 2, 3, ...
- The number -2.22 is not an integer because it has a fractional part (the decimal part).
- Thus, -2.22 is not an integer.
- Answer: False
4. Rational Numbers:
- Rational numbers are numbers that can be expressed as the quotient (or fraction) of two integers. In other words, a rational number can be written in the form [tex]\( \frac{p}{q} \)[/tex], where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers and [tex]\( q \neq 0 \)[/tex].
- The number -2.22 can be written as [tex]\( \frac{-222}{100} \)[/tex] (by multiplying and dividing by 100 to eliminate the fractional part).
- Therefore, -2.22 is a rational number.
- Answer: True
5. Irrational Numbers:
- Irrational numbers are numbers that cannot be expressed as the ratio of two integers. These include certain decimal numbers that do not terminate or repeat, such as π and √2.
- Since -2.22 can be expressed as a fraction [tex]\( \frac{-222}{100} \)[/tex], it is not an irrational number.
- Answer: False
6. Real Numbers:
- Real numbers include all rational and irrational numbers. This set constitutes all numbers that can be found on the number line, encompassing both rational and irrational numbers.
- Since -2.22 is a rational number, it is inherently also a real number.
- Answer: True
So, to summarize, the number -2.22 belongs to the following sets:
- Rational numbers
- Real numbers
The classifications for -2.22 are:
- Natural numbers: False
- Whole numbers: False
- Integers: False
- Rational numbers: True
- Irrational numbers: False
- Real numbers: True
