Number 7

4 marks · Normal

Study the decimal expansions below and answer the questions.

(a)

Which of the following decimals is recurring? Circle your answer. (i) 0.125 (ii) 0.27272727... (iii) 0.304

[1 mark]

(b)

Explain why.

[1 mark]

(c)

Write 0.27272727... as a fraction in its simplest form.

[2 marks]

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.

Show answer

(a) (ii) 0.27272727...

(b) It has a repeating block of digits ('27') after the decimal point.

(c)

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Identifies (ii) 0.27272727... as the recurring decimal.

B1 (b) · 1 mark · Explains the decimal is recurring because a pattern repeats indefinitely.

M1 (c) · 1 mark · Correctly sets up and forms the equation to convert 0.2727... to a fraction.

A1 (c) · 1 mark · Gives or for 0.272727…

Worked solution

a) 0.27272727... is the recurring decimal.

b) Because the block '27' repeats forever after the decimal point.

c) Let . Multiply both sides by 100: . Subtract: . . .