Question

Which of these numbers can be classified as both real and irrational?

5.85
63.4

Which statement is false?

The number zero is a rational number
some irrational numbers are also rational numbers
every irrational number is a real number
Every integer is a rational number.

Answer 1

1) Both are real number but not irrational number.

2) a) True b) False c) True d)True

Explanation:

We are given the following information in the question:

1) Both 5.85 and 63.4 are real numbers. But they are not irrational numbers as clear that their decimal expansion is clearly terminating.

2) a) True

As zero can be written in the form of a fraction
`(x)/(y), y \\eq 0`

b) False

No irrational numbers can be rational numbers. They both are different categories of numbers.

c)True

Real numbers is a collection of irrational number and real numbers.

d) True

Since every integer can be written in the form of a fraction
`(x)/(y), y \\eq 0`

Answer 2

Real numbers are any numbers aside from the imaginary numbers which include the set of rational, irrational numbers, maybe positive or negative and extending from negative infinity to positive infinity. Rational numbers are numbers that can be expressed as a ratio of two numbers. Among the choices, D. Every integer is a rational number is wrong as integers are whole numbers only.