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Name the set or sets of numbers to which each real number belongs.

-22

Short Answer

Expert verified

The real number -22belongs to the set of irrational numbers.

Step by step solution

01

Step-1. Apply the concept of the real number system

Real numbers include all the numbers except complex numbers and have the following five subsets:

  1. Natural numbers: Includes counting objects and starting from 1.
  2. Whole numbers: Includes the set of natural numbers along with 0.
  3. Integers: Z = Includes numbers that are not fraction (positive and negative whole numbers)
  4. Rational numbers: Includes the numbers which can be written in the form ofpq where p and q are integers, q0.
  5. Irrational numbers: Includes numbers that cannot be written in the form of pqwhere p and q are integers, q0.
02

Step-2. Examples of the real number system.

1. Natural numbers:1,2,3,4,...

2. Whole numbers:0,1,2,3,4,...

3. Integers: Measurement of debts, temperatures, etc., fall under the set of integers ...,-3,-2,-1,0,1,2,3,....

4. Rational numbers: If we cut a cake into equal pieces, then we may have a piece that represents a fraction like56,1.5=32,69,83.

5. Irrational numbers: The numbers that are square roots of positive rational numbers, cube roots of rational numbers, etc., such as2,53,-3.

03

Step-3. Analyze the given real number.

Consider the given real number-22

Now we will check each subset of real numbers:

  1. Natural numbers: They are positive, countable and start from 1. So,-22 not being a counting object is not a natural number.
  2. Whole numbers: They are natural numbers including 0. So,-22 not being a natural number is not a whole number as well.
  3. Integers: They are whole numbers that are both positive and negative. Since-22 is not a whole number, it is not an integer as well.
  4. Rational numbers: They can be written in the form pqwhere p and q are integers, q0. Since-22 cannot be written in the exact form, it is not a rational number.
  5. Irrational numbers: They cannot be written in the form pqwhere p and q are integers, q0. Since from the above point,-22 cannot be written in the form pq, it is an irrational number.

Therefore, the real number -22belongs to the set of irrational numbers.

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