AC9M8N03Year 8NumberPractised on site

AC9M8N03 — Year 8 Number

Official Curriculum Content Description:

recognise terminating and recurring decimals, using digital tools as appropriate

Worked Examples (1)

Example 1Converting Recurring Decimals to Fractions

Convert the recurring decimal

0.8\dot{9}

to a fraction in lowest terms.

Common mistake: Dividing by

10

100

, or

1000

instead of

9

99

90

, or

999

Correct Answer:

\frac{9}{10}

Worked Solution:

Let

x = 0.8\dot{9}

. Then

10x = 8.\dot{9}

and

100x = 89.\dot{9}

. Subtracting gives

90x = 81

, so

x = \frac{81}{90}

. Divide both parts by

9

to reach lowest terms:

\frac{9}{10}

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