Which statement about real numbers is true?

Which statement about real numbers is true?

• A. They include all rational and irrational numbers.
• B. They include only integers.
• C. They include only fractions.
• D. They include only positive numbers.

Answer: (A)

Real numbers are all the numbers that can be placed on the number line, and they consist of two kinds: rational numbers (numbers that can be written as a ratio of integers, like 3/4 or -2) and irrational numbers (numbers that cannot be written as such a ratio, like sqrt(2) or pi). Because every real number is either rational or irrational, the set of real numbers includes all rational and all irrational numbers. It also includes integers (which are rational), as well as non-integer numbers, and both negative numbers and zero, not just positives. So the statement that real numbers include all rational and irrational numbers is the true one. The other options wrongly limit the scope to only integers, only fractions, or only positive numbers.

Real numbers are all the numbers that can be placed on the number line, and they consist of two kinds: rational numbers (numbers that can be written as a ratio of integers, like 3/4 or -2) and irrational numbers (numbers that cannot be written as such a ratio, like sqrt(2) or pi). Because every real number is either rational or irrational, the set of real numbers includes all rational and all irrational numbers. It also includes integers (which are rational), as well as non-integer numbers, and both negative numbers and zero, not just positives. So the statement that real numbers include all rational and irrational numbers is the true one. The other options wrongly limit the scope to only integers, only fractions, or only positive numbers.