Canada Grade 8 MathUnderstanding Rational and Irrational Numbers

Which of the following numbers is an irrational number?

• 0.75

• 5

Answer explanation

An irrational number cannot be expressed as a fraction of two integers. Among the options, \(\sqrt{2}\) is irrational, while \(\frac{3}{4}\), 0.75, and 5 are all rational numbers.

• 0.3

• 0.33

• 0.333...

• 0.3333

Answer explanation

The fraction \( \frac{1}{3} \) represents a repeating decimal. When divided, it results in 0.333..., where the 3 repeats indefinitely. Thus, the correct answer is 0.333..., indicating the repeating nature of the decimal.

Which of the following is a rational number?

• 0.25

Answer explanation

A rational number can be expressed as a fraction of two integers. 0.25 is equivalent to 1/4, making it a rational number. In contrast, π, √3, and e are all irrational numbers.

Which of the following numbers is not a rational number?

• 0.5

• 2.75

Answer explanation

A rational number can be expressed as a fraction of two integers. √5 cannot be expressed this way, making it an irrational number. The other options, ½, 2.75, and 7/8, are all rational.

Answer explanation

To find the sum of \(\frac{1}{2}\) and \(\frac{2}{3}\), convert to a common denominator (6): \(\frac{3}{6} + \frac{4}{6} = \frac{7}{6}\). Thus, the correct answer is \(\frac{7}{6}\).

Which of the following is an example of an irrational number?

• 0.125

• 1.5

Answer explanation

An irrational number cannot be expressed as a fraction of two integers. Among the options, \(\sqrt{7}\) is irrational, while 0.125, \(\frac{22}{7}\), and 1.5 are rational numbers.

Answer explanation

To find the product of \(\frac{3}{4}\) and \(\frac{2}{5}\), multiply the numerators (3 * 2 = 6) and the denominators (4 * 5 = 20). This gives \(\frac{6}{20}\), which simplifies to \(\frac{3}{10}\). Thus, the correct answer is \(\frac{3}{10}\).

Which of the following numbers is a rational number?

• 0.333...

Answer explanation

0.333... is a rational number because it can be expressed as the fraction 1/3. In contrast, \sqrt{11}, \pi, and e are all irrational numbers, meaning they cannot be expressed as a fraction of two integers.

• 2

• 3

• 4

• 5

Answer explanation

The value of \( \sqrt{16} \) is the number that, when multiplied by itself, equals 16. Since \( 4 \times 4 = 16 \), the correct answer is 4.

Which of the following is an irrational number?

• 0.666...

• 1.25

Answer explanation

An irrational number cannot be expressed as a fraction of two integers. \(\sqrt{10}\) is irrational, while \(\frac{5}{9}\), 0.666..., and 1.25 are rational numbers.