Converting any recurring decimal to a fraction | Maths

Starter quiz

Calculate 0.32 × 0.12

'0.0384' ✓
Calculate 0.36 ÷ 0.12

'0.0432' ✓
Calculate 0.32 × 0.9

'0.288' ✓
Calculate 0.04 - 1.23

'-1.19' ✓
Which fraction is largest?

$\frac{3}{7}$

$\frac{9}{21}$

$\frac{7}{12}$ ✓
Which fraction is smallest?

$\frac{1}{10}$

$\frac{2}{21}$

$\frac{3}{33}$ ✓

Exit quiz

Which of these fractions is equivalent to $0.\dot{3}$ ?

$\frac{3}{10}$

$\frac{1}{3}$ ✓

$\frac{3}{90}$
Which of these fractions is equivalent to $0.\dot{0}\dot{9}$ ?

$\frac{1}{11}$ ✓

$\frac{9}{11}$

$\frac{1}{90}$
Which of these fractions is equivalent to $0.8\dot{3}$ ?

$\frac{8}{3}$

$\frac{83}{10}$

$\frac{5}{6}$ ✓
Which of these fractions is equivalent to $0.08\dot{3}$ ?

$\frac{1}{12}$ ✓

$\frac{83}{10}$

$\frac{5}{6}$
Which of these fractions is equivalent to $0.\dot{5}$ ?

$\frac{5}{10}$

$\frac{5}{11}$

$\frac{5}{9}$ ✓
Which of these fractions is equivalent to $0.0\dot{6}$ ?

$\frac{1}{15}$ ✓

$\frac{1}{6}$

$\frac{1}{60}$

Worksheet

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Lesson Details

Key learning points

A recurring decimal does not terminate.
By considering the infinite nature of recurring decimals, it is possible to create two equations.
These simultaneous equations can be combined to create a third valid equation.
This can be solved to find the fractional equivalent to the recurring decimal.
A calculator can help us investigate this conversion.

Common misconception

Assuming that the decimal part of the number will entirely disappear in the subtraction step.

Ensure that pupils line up the decimal points and use squares in their books for each digit. This should allow pupils to see the parts that cancel each other out and what is left when finding the difference.

Keywords

Recurring decimal - A recurring decimal is one that has an infinite number of digits after the decimal point.
Irrational number - An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.
Terminating decimal - A terminating decimal is one that has a finite number of digits after the decimal point.