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.