Represent numbers with powers
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Write 3207 in expanded notation using powers of 10.
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Answer: 3 × 10^3 + 2 × 10^2 + 7 × 10^0
- Match each non-zero digit to its place-value power of ten.
- 3207 = 3 × 10^3 + 2 × 10^2 + 7 × 10^0.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Use place-value powers and prime-power products.
Read the official VCAA curriculum description (VC2M7N02)
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- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M7N02-C01A digit contributes its value times a power of ten. The exponent counts places from the ones column, which is power zero.
- VC2M7N02-C02Repeatedly split composite factors until only primes remain, then combine repeated primes using exponent notation.
- VC2M7N02-C03A complete factor representation must multiply back to the starting value. Repeated primes are compressed notation, not a different product.
- VC2M7N02-C04Constructing and explaining both exponential representations.
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Descriptor-derived subskills
- D01Expand a natural numberA digit contributes its value times a power of ten. The exponent counts places from the ones column, which is power zero.
- D02Factor completely into primesRepeatedly split composite factors until only primes remain, then combine repeated primes using exponent notation.
- D03Check by rebuilding the productA complete factor representation must multiply back to the starting value. Repeated primes are compressed notation, not a different product.