Back to Know that numbers that are not rational are called irrational — Problem 4 · Task Set 1

8.NS.A.1 Tutor Intake -- Rational and Irrational Numbers

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Grade 8·11 problems·~12 min·Common Core Math - Grade 8·container·8-ns-a-1

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Concepts

$1/7 = 0.\overline{142857}$ has six digits in its repeating
block. Some students conclude this must be irrational because
the decimal "goes on forever" and looks complicated. What is the
flaw in that reasoning?

The reasoning is correct because $1/7$ cannot be written using a bar over the repeating digits.

There is no flaw — any decimal with six or more digits before it starts repeating is irrational.

"Going on forever" alone is not the test — the block $142857$ repeats indefinitely, so the decimal is eventually repeating, which makes $1/7$ rational.

The flaw is that $1/7$ actually terminates if you divide far enough.