Which statement about real numbers is true?

• A. Real numbers include both rational and irrational numbers.
• B. Real numbers include only integers.
• C. Real numbers include only fractions.
• D. Real numbers exclude negative numbers.

Answer: (A)

The real numbers are all the points you can place on the number line, including every rational and irrational number. Rational numbers are fractions of integers, which includes integers themselves like -3, 0, and 5, as well as fractions such as 1/2 or -7/4. Irrational numbers cannot be written as a ratio of integers, and their decimal expansions never terminate or repeat, examples being sqrt(2) and pi. Real numbers also include negative values, zero, and positives. Because real numbers contain both rational and irrational numbers and extend in both directions along the number line, the statement is true. The other descriptions—being limited to only integers, only fractions, or excluding negatives—don’t fit the full set of real numbers.