AC9M7N03 • Year 7 Maths • Number • Learn
represent natural numbers in expanded notation using place value and powers of 10.
We are learning to represent natural numbers in expanded notation using place value and powers of 10.
Place value assigns each digit a coefficient of a power of 10. In 7 052 304, the 7 is a coefficient of 10⁶, while the 5 is a coefficient of 10⁴.
Expanded notation records this structure explicitly. Zero coefficients may be omitted from the sum, but their place-value positions must remain intact when the numeral is reconstructed.
The pattern includes 10⁰ = 1, so the ones digit can be written as a coefficient of 10⁰. Converting in both directions checks that every digit is attached to the correct power of 10.
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 1
Final answer: 7 052 304 = 7×10⁶ + 5×10⁴ + 2×10³ + 3×10² + 4×10⁰.
Check: Adding the expanded terms reconstructs 7 052 304.
Example 2
Final answer: 6×10⁵ + 4×10³ + 8×10 + 2 = 604 082.
Check: Re-expand 604 082 and compare every coefficient.
Example 3
Problem: A number is written as 6×10⁵ + 4×10³ + 9×10 + 2. Write the numeral and explain the role of the zero place holders.
Final answer: The numeral is 604 092. Zero placeholders keep the hundred-thousands-to-ones place values aligned where no coefficient is present.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: Compare 9×10⁵ + 8×10² with 8×10⁵ + 9×10⁴. Which is greater?
Final answer: 900 800 is greater than 890 000 by 10 800.
Check: Compare the highest place where coefficients differ.
Common mistake: 10⁰ treated as zero.
Correction: 10⁰=1.
Common mistake: Exponents counted from one at the units place.
Correction: The units place is 10⁰.
Common mistake: Internal zeros removed from the numeral.
Correction: They preserve place even if their terms are omitted.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Evaluate 10⁰.
Answer: 10⁰ = 1.
Hint: Use the pattern 10², 10¹, 10⁰.
Why: A non-zero number to power zero equals one.
2. Write 4 205 in ordinary expanded notation.
Answer: 4 205 = 4 000 + 200 + 5.
Hint: Read each digit's place.
Why: Zero tens contribute no term.
3. Write 83 010 using powers of 10.
Answer: 83 010 = 8×10⁴ + 3×10³ + 1×10.
Hint: Label ten-thousands through ones.
Why: Each coefficient matches its place-value digit.
4. Write 7 052 304 using powers of 10.
Answer: 7×10⁶ + 5×10⁴ + 2×10³ + 3×10² + 4×10⁰.
Hint: Keep each digit attached to its original power.
Why: Zero coefficients may be omitted without shifting places.
5. Reconstruct 5×10⁵ + 9×10² + 6.
Answer: 500 906.
Hint: Create a place-value table.
Why: The missing thousands and tens positions contain zero.
6. What coefficient of 10³ appears in 2 347 018?
Answer: The coefficient is 7 because the thousands digit is 7.
Hint: Locate the thousands column.
Why: A coefficient is the digit multiplying a power of 10.
7. Correct: 60 405 = 6×10⁴ + 4×10³ + 5.
Answer: It should be 6×10⁴ + 4×10² + 5×10⁰.
Hint: Align digits with powers in a table.
Why: The digit 4 is in the hundreds place, not thousands.
8. A number is 3×10⁶ + a×10⁴ + 7×10² + 2. If it is 3 050 702, find a.
Answer: Matching place values gives a×10⁴=50 000, so a=5; substituting reconstructs 3 050 702.
Hint: Match coefficients place by place.
Why: The ten-thousands digit of 3 050 702 is five.
9. Compare 9×10⁵ + 8×10² with 8×10⁵ + 9×10⁴. Which is greater?
Answer: 900 800 is greater than 890 000 by 10 800.
Hint: Reconstruct both numerals before subtracting.
Why: Compare the highest place where coefficients differ.
10. A number is written as 6×10⁵ + 4×10³ + 9×10 + 2. Write the numeral and explain the role of the zero place holders.
Answer: The numeral is 604 092. Zero placeholders keep the hundred-thousands-to-ones place values aligned where no coefficient is present.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7N03 — represent natural numbers in expanded notation using place value and powers of 10 |
| Victoria | Victorian Curriculum F-10 | Year 7 Maths: closest match in Number. Use this page as a VIC-aligned practice and homework reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Represent natural numbers in expanded notation using place value and powers of 10 and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Represent natural numbers in expanded notation using place value and powers of 10. |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Represent natural numbers in expanded notation using place value and powers of 10. |
| Canada | Provincial and territory curricula | Grade 7 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 4 Maths: closest achievement-objective topic for Represent natural numbers in expanded notation using place value and powers of 10. |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Represent natural numbers in expanded notation using place value and powers of 10. |
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Khan Academy — Read powers of ten as repeated multiplication, then apply them in expanded place-value notation.
As you watch: What does the exponent tell you in a power of ten?
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Try it: Write 50,304 as a sum involving powers of ten and explain why the missing place contributes zero.
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Mapped skill: represent natural numbers in expanded notation using place value and powers of 10
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7N03 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N03 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-FRC-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M7N03 — Expanded Notation with Powers of 10
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