13 \(x = 0.\dot{2} \qquad y = 0.6\dot{8}\dot{1}\)

Work out the value of \(xy\).
Give your answer as a fraction in its simplest form. (5)

14 Prove algebraically that \(0.4\dot{6}\dot{2}\) can be written as \(\dfrac{229}{495}\) (3)

18 Show that \(0.\dot{1}\dot{5} + 0.2\dot{2}\dot{7}\) can be written in the form \(\dfrac{m}{66}\) where \(m\) is an integer. (3)

13 Prove algebraically that \(0.0\dot{7}2\dot{3}\) can be written as \(\dfrac{241}{3330}\) (3)

20 Prove algebraically that \(0.1\dot{2}\dot{3}\) can be written as \(\dfrac{61}{495}\) (3)

14 Using algebra, prove that \(1.06\dot{2}\) can be written as \(1\dfrac{14}{225}\) (3)

12 Express \(0.1\dot{1}\dot{7}\) as a fraction.
You must show all your working. (3)

13 Ted is trying to change \(0.\dot{4}\dot{3}\) to a fraction.

Here is the start of his method.

\(x = 0.\dot{4}\dot{3}\)
\(10x = 4.\dot{3}\dot{4}\)
\(10x - x = 4.\dot{3}\dot{4} - 0.\dot{4}\dot{3}\)

Evaluate Ted’s method so far. (1)

15 Express \(0.4\dot{1}\dot{8}\) as a fraction.
You must show all your working. (3)

16 Prove algebraically that \(0.2\dot{5}\dot{6}\) can be written as \(\dfrac{127}{495}\) (3)

15 \(x = 0.4\dot{3}\dot{6}\)

Prove algebraically that \(x\) can be written as \(\dfrac{24}{55}\) (3)

8 Write these numbers in order of size.
Start with the smallest number.

\(0.2\dot{4}\dot{6}\qquad\quad 0.24\dot{6}\qquad\quad 0.\dot{2}4\dot{6}\qquad\quad 0.246\) (2)

16 Using algebra, prove that \(0.1\dot{3}\dot{6} \times 0.\dot{2}\) is equal in value to \(\dfrac{1}{33}\) (3)

21 \(x = 0.0\dot{4}\dot{5}\)

Prove algebraically that \(x\) can be written as \(\dfrac{1}{22}\) (3)

24 Express the recurring decimal \(0.2\dot{8}\dot{1}\) as a fraction in its simplest form. (3)

12

21 Prove algebraically that \(\quad 1.0\dot{1}\dot{8} = \dfrac{56}{55}\) [3 marks]

19 When converted to a fraction \(\quad 0.\dot{7} = \dfrac{7}{9}\)

Work out \(\quad 0.\dot{4} + 0.0\dot{7}\)

Give your answer as a fraction. [3 marks]

8 Circle the largest number. [1 mark]

• \(5.30\dot{4}\)
• 5.344
• 5.34
• \(5.3\dot{4}\)

23 Write \(0.1\dot{3}\) as a fraction in its simplest form. [3 marks]

21 Convert \(\quad 0.6\dot{1} \quad\) to a fraction. [3 marks]

13 Work out \(\quad 0.4\dot{7} + 0.312\)

Circle your answer. [1 mark]

• 0.782
• 0.789
• \(0.789\dot{7}\)
• \(0.7\dot{8}\dot{9}\)

22 Work out \(\quad 0.6\dot{8} - 0.4\dot{5}\)

Give your answer as a fraction in its simplest form. [5 marks]

1 Circle the smallest number. [1 mark]

• 4.31
• \(4.\dot{3}\)
• 4.301
• 4.33

13 Convert \(\quad \dfrac{5}{6} \quad\) to a recurring decimal. [2 marks]

2 Circle the largest number. [1 mark]

• \(0.\dot{5}\)
• 0.55
• 0.545
• \(0.\dot{5}4\dot{5}\)

26 Prove algebraically that \(\quad 3.4\dot{7} = \dfrac{313}{90}\) [3 marks]

21 Work out \(\quad 0.70\dot{4}\dot{8} - 0.001\)

Circle your answer. [1 mark]

• \(0.70\dot{3}\dot{8}\)
• \(0.703\dot{8}\)
• \(0.703\dot{8}\dot{3}\)
• \(0.703\dot{8}\dot{4}\)

19 Circle the fraction that is equivalent to \(\quad 0.\dot{1}\) [1 mark]

• \(\dfrac{1}{9}\)
• \(\dfrac{1}{99}\)
• \(\dfrac{1}{10}\)
• \(\dfrac{11}{100}\)

27 Prove algebraically that \(\; 2.7\dot{5} \;\) converts to the fraction \(\dfrac{124}{45}\) [3 marks]

3 Circle the largest number. [1 mark]

• \(3.2\dot{7}\)
• 3.27
• 3.277
• \(3.20\dot{7}\)

26

15 \(\dfrac{1}{6}\), \(\dfrac{1}{7}\), \(\dfrac{1}{8}\) and \(\dfrac{1}{9}\) are four fractions.

How many of these fractions convert to a recurring decimal?

Circle your answer. [1 mark]

• 0
• 1
• 2
• 3
• 4

18 Work out.

Give your answer as a mixed number in its simplest form.

You must show your working. [5]

15 Prove that \(1.8\dot{6}\) converts to the fraction \(\dfrac{28}{15}\).
You must show your working. [3]

13 Write \(\dfrac{4}{11}\) as a recurring decimal. [2]

17 The diagram shows a number line.

P = \(1.\dot{2}\) and Q = \(1\frac{2}{3}\).

Q is the midpoint of PR.

Find the value of R.
Give your answer as a mixed number in its simplest form.
You must show your working. [5]

17

18 Work out.

Give your answer as a fraction in its simplest form. [4]

16

11 Write \(0.\dot{2}\dot{7}\) as a fraction in its simplest form. [3]

16 Work out \(0.\dot{6} \times 0.\dot{5}\dot{4}\) giving your answer as a fraction in its simplest form.
You must show your working. [5]

13

18 Write \(0.4\dot{1}\dot{6}\) as a fraction in its simplest form.
You must show full working in support of your answer. [3]

13

10

14

13

12

13