Concept 1

Work with rational and irrational numbers; compare magnitudes and order.

Compare rational and irrational numbers by using decimals or benchmarks on the same scale.

Core Idea

Put unlike numbers on the same scale before comparing them. Convert fractions, radicals, and constants to nearby decimals or use strong benchmarks.

Understanding

Rule: This skill is less about computation and more about number sense.

Fractions, decimals, radicals, and irrational constants can all represent values in the same range, so compare their sizes, not their forms. On the ACT, quick benchmark values such as $\sqrt 4 = 2$ , $\sqrt 9 = 3$ , $𝜋 \approx 3.14$ , and common fraction-decimal pairs save time and reduce guesswork.

Question

Worked Example

Which list is in order from least to greatest: $𝜋 2, 2.2, \sqrt 5, 94$ ?

Select an answer to see the explanation