8th Grade Rational and Irrational Numbers Test with Point Values (PDF)

1. Write \(\frac{7}{8}\) as a decimal. (1 point)
2. Write \(\frac{4}{9}\) as a decimal using a bar. (1 point)
3. Is \(\frac{7}{8}\) rational? Explain. (1 point)

1. Write \(0.\overline{5}\) as a fraction. (1 point)
2. Write \(0.\overline{18}\) as a fraction in lowest terms. (2 points)

Point P marks \(\sqrt{31}\) on the number line. Between which two integers does \(\sqrt{31}\) lie? Write the integers.

Estimate \(\sqrt{31}\) to the nearest tenth.

Write rational or irrational for each number.

1. \(\sqrt{81}\)
2. \(\sqrt{15}\)
3. \(0.\overline{72}\)
4. \(2\pi\)

Order from least to greatest: \(\sqrt{10}\), \(3.1\), \(\frac{16}{5}\), \(3.\overline{2}\).

1. Compare \(\sqrt{75}\) and \(8.7\) using \(<\) or \(>\). (1 point)
2. Compare \(\pi\) and \(3.14\). (1 point)

1. Write an expression for the side length. (1 point)
2. Between which integers is the side length? (1 point)
3. Find the side length to the nearest tenth of a foot. (1 point)

Maya says \(0.\overline{9}\) is irrational because it never ends. Is she correct? Show a calculation.