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2/3
9x=6.
O Level · English Medium · Cambridge · Mathematics
Number, fractions, decimals and percentages
Combine recurring decimals, index laws and percentage reversal.
About this lesson and its coverage
Original Kidemy O Level progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
Use place-value shifts to turn a recurring decimal into an equation. Apply index laws only under their stated base restrictions. Reverse percentage problems divide by a multiplier; an exact intermediate fraction can make the check clearer.
Worked example
For x=0.333...,10x−x=3, so x=1/3. A price after a 15% reduction is 85% of its original.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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200
170/0.85.
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9
3^−2=1/9.
Write in your own words. A guardian or teacher should review this response.
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100x−x=12 gives 99x=12, so x=4/33.
Use a shift matching the two-digit repeat.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
Extra digits can exceed the precision of the given data or model.
Connect precision to evidence.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Solve one recurring-decimal and one reverse-percentage problem with exact checks.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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