Back to Use rational approximations of irrational numbers — Problem 2 · Task Set 3

8.NS.A.2 Tutor Intake -- Rational Approximations of Irrational Numbers

This short check helps your tutor see where to start. Work each problem on
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every answer helps your tutor plan your first few sessions.

Grade 8·10 problems·~11 min·Common Core Math - Grade 8·container·8-ns-a-2

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Concepts

A student says: "I can't plot $\sqrt{2}$ on a number line because
we don't know its exact decimal value." Is this reasoning
correct?

Yes — since we cannot write the exact decimal, the number does not have one specific location and cannot be plotted accurately.

No — $\sqrt{2}$ has a precise, exact location on the number line (e.g., the diagonal of a unit square); we just approximate that location using rational bounds like 1.41 to 1.42, which is precise enough to plot.

No — but only whole numbers and simple fractions can be plotted accurately; $\sqrt{2}$ can only be plotted roughly, in the wrong place.

Yes — irrational numbers are not real numbers, so they don't belong on the real number line at all.