Real numbers, order and absolute value

Build a precise understanding of real numbers before beginning algebraic manipulation. This practice set develops number-set classification, the meaning of rational and irrational numbers, decimal representations, ordering, absolute value and distance on a number line. It gives particular attention to distinctions that later affect algebra: a value versus its magnitude, an exact number versus an approximation, and distance versus signed change.

The questions begin with recognition and interpretation, then move toward comparisons, applications and counterexamples. You will encounter both single-answer and select-all formats. Work out the mathematical reason before relying on the choices, and check each statement independently when several answers may be correct. Where a convention about natural numbers matters, it is stated explicitly.

Only numerical absolute values are used here; solving absolute-value equations belongs to a later module. Basic familiarity with whole numbers and decimal notation is helpful. After each attempt, use the explanations to identify whether an error came from signs, place value, classification or the meaning of distance. This foundation supports the next set on signed arithmetic and fractions and prepares you to interpret domains, inequalities and graphs later in precalculus.