Year 10 - Maths
Converting any recurring decimal to a fraction
Arithmetic procedures: index laws
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.
Lesson Summary
You will learn to appreciate the infinite nature of recurring decimals and can convert between a recurring decimal and a fraction.
Key Notes
- 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.
Vocabulary To Learn
- 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.
Common Mistakes To Avoid
- Assuming that the decimal part of the number will entirely disappear in the subtraction step.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A recurring decimal does not terminate. By considering the infinite nature of recurring decimals, it is possible to create two equations.
2. Use this key word in a maths sentence and explain it clearly. 'Recurring decimal'
A recurring decimal is one that has an infinite number of digits after the decimal point. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Assuming that the decimal part of the number will entirely disappear in the subtraction step. Correction: 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.
More Lessons In This Unit
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculating with fractions and decimals Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Problem solving with the laws of indices Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
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