Year 8: Recurring decimals

What are recurring decimals?

Recurring decimals (also called repeating decimals) are decimals that go on forever but follow a repeating pattern.

Examples:
1 ÷ 3 = 0.333... (or 0.3)
2 ÷ 11 = 0.181818... (or 0.18)

We use a bar (‾) to show the repeating part:
0.333... = 0.3
0.181818... = 0.18

Types of recurring decimals:

• Pure recurring – all digits repeat: 0.̅6, 0.̅123
• Mixed recurring – some digits don’t repeat at first: 0.16, 0.254

Converting fractions to decimals:

• Divide the numerator by the denominator.
• If the decimal doesn’t end, check for a repeating pattern.

Converting recurring decimals to fractions:

Let x = 0.3
Then 10x = 3.3
Subtract: 10x - x = 9x = 3
So x = 3 ÷ 9 = 1/3

Remember:

All recurring decimals are rational numbers — they can be written as fractions.

Look for patterns and use bar notation to simplify your work.