Study Notes
Recurring decimals are numbers with infinitely repeating digits after the decimal point. They can be expressed as fractions, which are the simplest form of rational numbers.
- Recurring Decimal — a number containing an infinitely repeating digit after the decimal point. Example: 0.4444... can be expressed as 4/9.
- Rational Number — a number that can be expressed as a fraction of two integers. Example: 1/2 is a rational number.
- Irrational Number — a number that cannot be expressed as a division of two integers. Example: √2 is an irrational number.
Exam Tips
Key Definitions to Remember
- Recurring Decimal: A decimal with repeating digits.
- Rational Number: A number expressible as a fraction of two integers.
- Irrational Number: A number not expressible as a fraction of two integers.
Common Confusions
- Confusing recurring decimals with finite decimals.
- Assuming all decimals are irrational numbers.
Typical Exam Questions
- What is a recurring decimal? A decimal with repeating digits.
- How do you express 0.818181... as a fraction? 81/99 or simplified to 9/11.
- Is 0.41 a rational number? Yes, because it can be expressed as 41/100.
What Examiners Usually Test
- Converting recurring decimals to fractions.
- Distinguishing between rational and irrational numbers.
- Understanding the concept of repeating digits in decimals.