Answer:
8) Real; Rational
9) Real; Rational; Integer; Whole; Natural
10) Real; Rational
Step-by-step explanation:
Real numbers consists of the subsets:
Irrational Numbers:
Irrational numbers is the subset complementary to rational numbers. It includes numbers such as √(2) or π. These numbers do not repeat nor terminate.
Rational Numbers:
Rational numbers are all the others. They include the integers as well as the repeating and terminating decimals.
Integers:
Integers include the entire set of whole numbers and the negative numbers. This subset does not include decimals nor fractions. Thus, the integers are: ...-3, -2, -1, 0, 1, 2, 3... etc.
Whole Numbers:
Whole numbers is the set of natural numbers that includes 0. So, whole numbers are: 0, 1, 2, 3... and so on.
Natural Numbers:
Natural numbers or the counting numbers are all the positive, non-decimal numbers. These are 1, 2, 3... and so on. This set does not include 0.
8) [tex]1.\overline{3}=1.3333...[/tex]
The given number is not natural, whole, nor an integer because it is a decimal. It repeats, so it belongs to the rational numbers subset.
9) [tex]\sqrt4=2[/tex]
The square root of 4 is simply 2. 2 is a natural number. Because of this, this means that 2 is also a whole number, integer, and a rational number.
10)[tex]-3/4=-0.75[/tex]
The given number is a fraction and it does not reduce to a whole number, so it's not a natural number, whole number, nor an integer. It does terminate, so it belongs to the rational numbers subset.
