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

-5419

Short Answer

Expert verified

The real number -5419belongs to the set of rational 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 of pq 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 like 56,1.5=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-5419

Now we will check each subset of real numbers:

  1. Natural numbers: They are positive, countable, and start from 1. So, -5419not being a positive number is not a natural number.
  2. Whole numbers: They are natural numbers including 0. So, -5419not being a natural number is not a whole number as well.
  3. Integers: They are numbers that are not a fraction. Since -5419is a proper fraction, it is not an integer.
  4. Rational numbers: They can be written in the form pqwhere p and q are integers, q0. Since -5419is the exact form, it is 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, can be written in the form pq, it is not an irrational number.

Therefore, the real number -5419belongs to the set of rational numbers.

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