lesson
Subtract matching recurring tails
1 · Learn
A recurring decimal represents an exact rational value. Multiplying by a suitable power of ten aligns the recurring tails, allowing subtraction to remove them. The number of repeated digits determines the useful power.
Distinguish an infinite recurring decimal from a rounded finite display. Replacing the former by a few written digits before calculating changes the value.
2 · Worked example
Thus x = 27/99 = 3/11. The repeating two-digit block is removed by subtracting x from 100x.
3 · Your turn
Convert 0.4444... to an exact fraction.
Check your answer
Let x = 0.4444...; 10x - x = 4, so x = 4/9.
4 · Apply your learning
Explain why 0.44 is not exactly 4/9 even though it begins with the same digits.
Adult guidance and safety
This sequence includes extension mathematics and assumes secure earlier work. Check prerequisite understanding and the learner's readiness before assigning extension tasks. Require derivations, accurate diagrams and varied practice; a correct short example is not full assessment evidence. Exam-board and tier-specific pathways are outside this edition.
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