Question

Check each set that includes the number shown 5/9 a. natural numbers b.whole numbers c.integers d. rational numbers e.irrational numbers f.real numbers

Answer 1

5/9 from these categories can only be classified as rational and real.

Explanation:

Natural numbers are counting numbers. People don't ever say the number 5/9 when counting people. So 5/9 is not natural.

Whole numbers are counting numbers plus also including 0. So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.

Integers are whole numbers plus the opposite of the whole numbers. 5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.

Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.

Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.

Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.

Answer 2

d. Rational Numbers

f. Real Numbers

Explanation:

The number shown is 5/9

Let us see the options one by one

a. Natural numbers

Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.

b. Whole numbers

Whole numbers is the set of natural numbers along with zero so it is also not the right answer.

c. Integers

Integers are combination of negative and positive whole numbers hence it is also not correct.

d. Rational numbers

Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.

e. As the number is rational, it cannot be irrational

f. Real numbers

As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..