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

An irrational number cannot be written as a ratio of two integers, no matter how hard you try — but it is still an exact, precise real number.

An irrational number is any number with a long or complicated-looking decimal.

An irrational number is a number that mathematicians have not yet found a fraction for, but one probably exists.

An irrational number is not a real number — it only exists as a rounded approximation, like 1.41 for $\sqrt{2}$.

Irrational — it terminates instead of repeating, so it does not meet the "repeating decimal" test for rational numbers.

Rational — $0.25 = 0.25000...$, and the repeating block "0" still counts as repeating, plus $0.25 = 1/4$ directly.

Rational — but only because it is short, not because of any repeating pattern.

It cannot be classified without a calculator.

Rational — $\sqrt{9} = 3$, and 3 can be written as $3/1$, a ratio of two integers.

Irrational — any number under a square root symbol is irrational.

Rational — but only because 9 is an even number.

Irrational — square roots never terminate.

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.

It always repeats — terminating decimals are actually irrational.

It terminates, or it goes on forever with no pattern at all.

It always terminates — repeating decimals are a sign of an irrational number.

It terminates (ends in repeating zeros), or it eventually repeats a fixed block of digits.