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1/16
Negative index means reciprocal.
Class 8 · English Medium · Cambridge · Mathematics
Number, fractions, decimals and percentages
Use index laws and standard form without losing the size of a number.
About this lesson and its coverage
Original Kidemy Class 8 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
For a nonzero base, a^m/a^n=a^(m−n); a negative index means a reciprocal. Standard form writes a number as c×10^n with 1≤c<10. Check whether an operation should make the result larger or smaller.
Worked example
2^−3=1/8. 0.00072=7.2×10^−4. (3×10^4)(2×10^3)=6×10^7.
- 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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12000
300×40.
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1
For a nonzero base, the zero power is 1.
Write in your own words. A guardian or teacher should review this response.
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It means 1/10³=0.001; the exponent does not put a minus sign on the value.
Explain reciprocal notation.
Write in your own words. A guardian or teacher should review this response.
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5.6×10^−5; move the decimal 5 places right to get5.6, so the power compensates with 10^−5.
Keep coefficient in the required range.
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Notebook challenge, sources and further study
Apply the idea
Estimate an index calculation before evaluating it and explain the scale.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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