Use the list below to classify all the subsets of real numbers to which the number “-29” belongs. – Real numbers – Irrational numbers – Rational numbers – Integers – Whole numbers – Natural numbers
The Correct Answer and Explanation is:
The number –29 belongs to the following subsets of real numbers:
- Real numbers
- Rational numbers
- Integers
Explanation:
To classify the number –29, let us consider each subset of the real number system and determine if it includes –29:
- Real numbers:
This is the broadest category. Real numbers include all rational and irrational numbers. Since –29 is a number that can be located on the number line, it is a real number. - Irrational numbers:
Irrational numbers are numbers that cannot be written as a simple fraction or ratio of two integers. Their decimal forms are non-repeating and non-terminating, such as π or √2.
–29 is not irrational because it can be written as a fraction: –29/1. So this set does not include –29. - Rational numbers:
Rational numbers are numbers that can be written as a ratio of two integers (a fraction), where the denominator is not zero. Since –29 = –29/1, it is a rational number. - Integers:
Integers include all whole numbers and their negative counterparts. The set of integers is {… –3, –2, –1, 0, 1, 2, 3, …}.
–29 is a negative whole number, so it is an integer. - Whole numbers:
Whole numbers are the non-negative integers: 0, 1, 2, 3, and so on.
–29 is not a whole number because it is negative. - Natural numbers:
Natural numbers are the counting numbers: 1, 2, 3, 4, and so on. Some definitions include 0, but all agree that negative numbers are not natural.
–29 is not a natural number.
Final classification:
–29 is a real number, a rational number, and an integer. It is not an irrational number, whole number, or natural number.
