Number 10

4 marks · Hard

State for each of the following numbers whether it is rational or irrational. If rational, write it as a fraction in the form , where and are integers. Show full reasoning.

(a)

(the decimal repeats with 25)

[1 mark]

(b)

[1 mark]

(c)

[1 mark]

(d)

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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(a) Rational;

(b) Irrational

(d) Irrational

Common mistakes: Stating is rational; Stating is rational

Show mark scheme and worked solution

Marking points

A1 (a) · 1 mark · Correctly identifies (a) as rational and gives it as or equivalent

A2 (b) · 1 mark · Correctly states (b) is irrational

A3 (c) · 1 mark · Correctly identifies (c) as rational and gives it as or equivalent

A4 (d) · 1 mark · Correctly states (d) is irrational

Worked solution

(a) is a recurring decimal, so it is rational. Let .

(b) is not the square root of a perfect square so is irrational.

(d) is rational, but is irrational. The sum of a rational and an irrational number is always irrational, so is irrational.