Which set includes every rational and irrational number?

• A. Real numbers
• B. Natural numbers
• C. Whole numbers
• D. Integers

Answer: (A)

Understanding how these number sets relate helps here: a rational number is a number that can be written as a fraction of integers, like 3/4 or -5/2, while an irrational number cannot be written as such a fraction, and its decimal goes on forever without repeating, like √2 or π. The real numbers include every number you can place on the number line, which means they contain both rationals and irrationals.

The other sets never include irrationals. Natural numbers are the counting numbers; they’re all rational but exclude irrationals. Whole numbers add zero to the naturals, still missing irrational values. Integers include positive, negative, and zero, but they are all rational as well. Since only the real numbers encompass both rational and irrational numbers, this is the best choice.