Number 10

4 marks · Normal

Consider the numbers:

(a)

Write each number (A, B, C, D) as either rational or irrational.

[2 marks]

(b)

State the value of B.

[1 mark]

(c)

Explain why D is irrational.

[1 mark]

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Show answer

(a) —

(b) 6

Common mistakes: Misclassifying recurring/terminating decimals; Not giving a reason for irrationality in D

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Correctly classifies two or three of A, B, C, D as rational/irrational.

B2 (a) · 1 mark · All four numbers correctly classified.

A1 (b) · 1 mark · States the value of B correctly as 6.

B3 (c) · 1 mark · Explains D is non-terminating and non-repeating (not recurring/terminating decimal).

Worked solution

A: 0.333... is a recurring decimal, so it is rational.

B: , which is an integer and thus rational.

C: is not a perfect square root, so it is irrational.

D: 2.505505550... is a decimal that does not terminate or repeat. It is irrational.