Rational and Irrational Numbers: Grade 8 Math Test – PDF Download

Question 1: Classify and justify (2 points)

Tell whether each number is rational or irrational. Justify each answer.

1. \(\sqrt{64}\) (1 point)
2. \(\sqrt{27}\) (1 point)

Question 2: Fractions as decimals (2 points)

Write each fraction as a decimal.

1. \(\frac{9}{16}\) (1 point)
2. \(\frac{4}{15}\) (1 point)

Question 3: Repeating decimals to fractions (3 points)

Write each repeating decimal as a fraction in simplest form.

1. \(0.\overline{18}\) (1 point)
2. \(0.4\overline{3}\) (2 points)

Question 4: Square root of 75 (3 points)

Consider \(\sqrt{75}\).

1. Between which two consecutive integers is \(\sqrt{75}\)? (1 point)
2. Estimate \(\sqrt{75}\) to the nearest tenth. (2 points)

Question 5: Match points on a number line (2 points)

Points A, B, C and D are on the number line.

1. Which point best represents \(\sqrt{10}\)? (1 point)
2. Which point best represents \(\sqrt{13}\)? (1 point)

Question 6: Compare numbers (2 points)

Compare each pair using \(<\), \(>\) or \(=\).

1. \(\sqrt{20}\) and \(4.5\) (1 point)
2. \(\pi\) and \(\frac{22}{7}\) (1 point)

Question 7: Order from least to greatest (2 points)

Write in order from least to greatest: \(\sqrt{5}\), \(2.2\), \(\frac{9}{4}\), \(2.\overline{3}\).

Question 8: Patio side length (2 points)

A square patio has an area of 55 square feet. Find the side length to the nearest tenth of a foot.

Question 9: Pattern decimal (2 points)

Sofia says that \(0.121221222122221\)… (one 2 more each time after each 1) is rational because it follows a pattern. Is she correct? Explain.

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