8th Grade Rational and Irrational Numbers Quiz: 10 Questions with Explanations

A \(\sqrt{16}\)B \(\sqrt{17}\)C \(\frac{17}{4}\)D \(0.\overline{17}\)

17 is not a perfect square, so its root never ends or repeats. \(\sqrt{16} = 4\) is rational.

A \(\frac{3}{10}\)B \(\frac{3}{100}\)C \(\frac{1}{30}\)D \(\frac{1}{3}\)

Let x = 0.333…; then 10x – x = 3, so x = 3/9 = 1/3. Using 3/10 forgets the repeat.

A 9 and 10B 8 and 9C 10 and 11D 44 and 46

\(9^{2} = 81\) and \(10^{2} = 100\), and 90 is between them. Halving 90 gives the wrong 45.

A \(\sqrt{5}\)B \(\sqrt{7}\)C \(\sqrt{8.5}\)D \(\sqrt{4}\)

A is near 2.65 and \(2.65^{2} \approx 7\). \(\sqrt{4} = 2\) is at the left end.

A \(\frac{9}{25}\)B \(\frac{4}{11}\)C \(\frac{36}{99}\)D \(\frac{3}{11}\)

\(0.\overline{36} = \frac{36}{99}\), and dividing top and bottom by 9 gives \(\frac{4}{11}\). The fraction 36/99 is not in lowest terms.

A \(\sqrt{30} > 5.5\)B \(\sqrt{30} = 5.5\)C \(5.5 > \sqrt{30}\)D Cannot be compared

\(5.5^{2} = 30.25 > 30\), so 5.5 is larger.

A Both are irrationalB Only 1.5 is rationalC Only 2.5 is rationalD Both are rational

1.5 = 3/2 and 2.5 = 5/2 are fractions of integers.

A \(2.\overline{14}\)B \(2.141141114…\)C \(\pi – 1\)D \(\sqrt{2} + 1\)

A repeating decimal is rational. The pattern 2.141141114… never repeats.

A 4.5 inB 4.0 inC 5.0 inD 10 in

\(4.5^{2} = 20.25\). Dividing 20 by 2 gives the wrong 10.

A \(\frac{157}{50}\)B \(\frac{3}{1}\)C \(\frac{22}{7}\)D \(\frac{314}{100}\)

22/7 = 3.1428… is above 3.14159… The others are 3.14, 3, 3.14.