Classify and interpret natural, whole, integer, rational, irrational, and real numbers, including their containment relationships, decimal forms, signs, magnitudes, units, and contextual meanings. Compare, order, and locate real numbers on a number line, including integers, fractions, terminating or repeating decimals, square roots, and familiar irrational numbers such as $\sqrt{2}$, $\sqrt{3}$, and $\pi$, using rational bounds and appropriate decimal approximations. Evaluate real-number expressions by applying grouping symbols, exponents, roots, and operations in the correct order, distinguish exact values from estimates, recognize undefined operations, and solve contextual problems while checking units, signs, magnitude, and reasonableness.