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Year 8 Maths • AC9M8N03 • Authored homework

Terminating and recurring decimals

Practise Terminating and recurring decimals through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.

10
Short-answer questions
10
Long-answer questions
1
Research/application task

Part A

Short-answer questions

  1. Convert 3/8 to a decimal and state whether it terminates or recurs.

  2. Convert 2/3 to recurring decimal notation.

  3. Explain how a calculator can help identify a recurring decimal, but also why reasoning is needed.

  4. A student says 0.333 is exactly 1/3. Correct the statement.

  5. Write the rule or formula most useful for Terminating and recurring decimals.

  6. Show how to check one answer using estimation, substitution or inverse operations.

  7. Write one common mistake students make in Terminating and recurring decimals and correct it.

  8. Create a small table, diagram or equation that represents this topic.

  9. State where units, exact form or rounding matter in this topic.

  10. Write one exam-style short question on Terminating and recurring decimals and solve it.

Part B

Long-answer questions

  1. Classify 7/20, 5/6, 11/25 and 4/9 as terminating or recurring decimals and justify each one.

  2. Compare 0.4, 0.44, 0.444... and 4/9 on a number line.

  3. Solve a multi-step problem involving Terminating and recurring decimals and explain every step clearly.

  4. Create a realistic word problem for Terminating and recurring decimals, solve it and interpret the answer.

  5. Compare two methods for a problem in Terminating and recurring decimals and explain which is more efficient.

  6. Write a worked solution that includes a check for reasonableness.

  7. Create a problem with a deliberate trap, then solve it correctly and explain the trap.

  8. Use a diagram, table, graph or equation to model a situation involving Terminating and recurring decimals.

  9. Explain how this topic connects to a previous Year 7 or Year 8 maths skill.

  10. Write a full-mark response to a challenging Terminating and recurring decimals question, including reasoning and final answer.

Part C

Research and understanding task

Research how recurring decimals are written in textbooks or calculators, then explain two notations with examples.