Study Notes
Recurring decimals are numbers with infinitely repeating digits after the decimal point. They can be expressed as fractions, showing they are rational numbers.
- Recurring Decimal — a decimal with a repeating sequence of digits. Example: 0.4444... can be written as 4/9.
- Finite Decimal — a decimal with a limited number of digits. Example: 0.5 is a finite decimal.
- Irrational Number — a number that cannot be expressed as a fraction of two integers. Example: √2 is an irrational number.
Exam Tips
Key Definitions to Remember
- Recurring Decimal: A decimal with a repeating sequence of digits.
- Finite Decimal: A decimal with a limited number of digits.
- Irrational Number: A number that cannot be expressed as a fraction of two integers.
Common Confusions
- Mistaking a recurring decimal for an irrational number.
- Confusing finite decimals with recurring decimals.
Typical Exam Questions
- What is a recurring decimal? A decimal with a repeating sequence of digits.
- How do you convert 0.818181... to a fraction? It can be expressed as 81/99, which simplifies to 9/11.
- Is 0.41 a rational number? Yes, because it can be expressed as a fraction.
What Examiners Usually Test
- Ability to convert recurring decimals to fractions.
- Understanding the difference between rational and irrational numbers.
- Identifying whether a number is finite, recurring, or irrational.