知识点 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.

核心知识

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

深入理解

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.

题目

示例解析

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

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