Task Sets: Know that numbers that are not rational are called irrational - Common Core Math - Grade 8

Recall / Warm-Up

These problems review skills you already know.

Which of these is the definition of a rational number?

A number that can be written as $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$ .

Any number with a decimal point.

A number that goes on forever.

A whole number only.

Which of these numbers is irrational?

$\frac{7}{8}$

$\sqrt{2}$

$0.25$

$-4$

Use long division to write $\frac{3}{8}$ as a decimal.

Fluency Practice

Classify each number or perform the conversion. Show your reasoning.

Classify $\sqrt{9}$ as rational or irrational.

Rational, because $\sqrt{9} = 3 = \frac{3}{1}$ , a ratio of integers.

Irrational, because it contains a square-root sign.

Classify $2 + \sqrt{2}$ as rational or irrational.

Irrational, because adding the rational number $2$ to the irrational number $\sqrt{2}$ gives an irrational result.

Rational, because $2$ is rational and the sum of any two numbers is rational.

The fraction $\frac{1}{7}$ equals $0.\overline{142857}$. Which describes its decimal expansion?

It terminates after a few digits.

It eventually repeats, so the number is rational.

It never repeats, so the number is irrational.

It is irrational because the block is long.

When you convert $\frac{1}{q}$ to a decimal by long division, the possible nonzero remainders are $1, 2, \ldots, q-1$ . For $q = 11$ , what is the greatest number of digits the repeating block could possibly have?

Convert the repeating decimal $0.\overline{4}$ to a fraction in simplest form.

Exercises: Rational and Irrational Numbers

Recall / Warm-Up

Fluency Practice