Question

Which of the following sets includes only rational numbers?

a) -5
b) 3/2
c) √49
d) 4.5

Answer 1

All the given options, -5, 3/2, √49, and 4.5, are examples of rational numbers because they can all be expressed as fractions with an integer numerator and a non-zero integer denominator.

Step-by-step explanation:

The question asks which of the following sets includes only rational numbers:

• a) -5
• b) 3/2
• c) √49
• d) 4.5

Rational numbers are any numbers that can be expressed as the quotient or fraction ⅟ where “p” and “q” are integers and “q” is not equal to zero. A rational number can be written as a simple fraction (example: 3/2) or a decimal that is either terminating (example: 4.5) or repeating.

Now, let's evaluate the options provided:

a) -5 can be written as -5/1 which is a quotient of two integers, so it is rational.

b) 3/2 is already in the form of a quotient of two integers, so it is rational.

c) √49 equals 7, which can be expressed as 7/1, so it is rational.

d) 4.5 can be expressed as 9/2 (since 4.5 = 4½), which is a quotient of two integers, so it is rational.

All four options a, b, c, and d are examples of rational numbers.