Optional enrichment: Remaining fractions, rates, recurring decimals and rational relationships
Example 1
Write 0.7828282… as a fraction. The digit 7 occurs once; the two-digit block 82 then repeats forever.
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Answer: 198155
- Let the number be x.
- Subtract 10x from 1000x to cancel the recurring tail: 990x=775.
- Divide by 990 and simplify.
Example 2
A tank contains pure juice. Drain 41 of its contents and replace it with water, mixing fully. Repeat this process once more. What fraction of the final mixture is water?
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Answer: 167
- The juice fraction is multiplied by 43 twice.
- Water therefore occupies 1−(43)2=167.
Example 3
Write 0.4404040… as a fraction. The digit 4 occurs once; the two-digit block 40 then repeats forever.
Show worked answer
Answer: 495218
- Let the number be x.
- Subtract 10x from 1000x to cancel the recurring tail: 990x=436.
- Divide by 990 and simplify.