Back to The Number System — Problem 2 · Task Set 37

8.NS Tutor Intake — Irrational Numbers and Rational Approximation

This short check helps your tutor find where to start. Answer each question without help — no calculator unless a problem says otherwise. If you're not sure, give your best try; the goal is to find what to work on together, not to grade you.

Grade 8·8 problems·~12 min·Common Core Math - Grade 8·domain·ns

Work through problems with immediate feedback

Concepts

Every real number has a decimal expansion. A rational number's
expansion terminates or eventually repeats; an irrational number's
expansion is infinite and never repeats. Which of the following
decimal expansions belongs to an irrational number?

$0.142857142857\ldots$ (the block $142857$ repeats)

$0.250000\ldots$

$0.1010010001\ldots$ (one more $0$ between each pair of $1$ s, forever)

$0.8333\ldots$ (the digit $3$ repeats)