AC9M7N05 • Year 7 Maths • Number • Learn
round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions.
We are learning to round decimals to a given accuracy appropriate to the context and use rounding and estimation to check the reasonableness of solutions.
Rounding replaces a value with a nearby value at a stated accuracy. Decimal places count positions after the decimal point, while significant figures begin at the first non-zero digit.
The context determines defensible accuracy: a travel distance may be reported to kilometres, while a measured dose may require tenths of a millilitre. Unnecessary digits can imply precision that the measurement does not support.
Estimation checks reasonableness before or after an exact calculation. Compatible numbers expose incorrect magnitude, and rounding bounds describe the interval of original values that would produce a reported result.
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: 47.386 rounds to 47.39 to two decimal places.
Check: The error 0.004 is less than 0.005.
Example 2
Final answer: The product should be about 1000, not 96.426.
Check: The exact product 964.26 is close to the estimate.
Example 3
Problem: A distance is reported as 8.4 km correct to the nearest 0.1 km. Give the interval of possible actual distances and decide whether 8.46 km could have produced the report.
Final answer: The actual distance satisfies 8.35 ≤ d < 8.45 km. Therefore 8.46 km could not round to 8.4 km to the nearest 0.1 km.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: A 12.48 m board is cut into 7 equal pieces. Estimate and calculate each length to the nearest centimetre.
Final answer: Estimate 12.6÷7=1.8 m; exact 12.48÷7≈1.783 m, which is 178 cm to the nearest centimetre.
Check: The requested nearest-centimetre accuracy controls the final rounding.
Common mistake: Significant figures confused with decimal places.
Correction: Count from the first non-zero digit for significant figures.
Common mistake: Rounding repeated at every step.
Correction: Keep guard digits and round at the end.
Common mistake: Units omitted.
Correction: Accuracy has meaning only with quantity and unit.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Round 8.746 to one decimal place.
Answer: 8.7.
Hint: Inspect the digit immediately to the right.
Why: The hundredths digit 4 does not round the tenths up.
2. Round 3 482 to the nearest hundred.
Answer: 3 500.
Hint: Mark the hundreds digit first.
Why: The tens digit 8 rounds the hundreds up.
3. Round 0.006784 to two significant figures.
Answer: 0.0068.
Hint: Count from 6, not from the decimal point.
Why: Significant figures begin at the first non-zero digit.
4. A journey is 186.7 km. Give a sensible whole-kilometre report.
Answer: 187 km.
Hint: Round to the nearest kilometre.
Why: Whole kilometres suit a general travel-distance report.
5. A medicine dose is 2.46 mL and must be measured to 0.1 mL. State the dose.
Answer: 2.5 mL.
Hint: Round to one decimal place.
Why: The stated measuring precision determines rounding.
6. Estimate 398×51 and use it to check a reported answer of 2 029.8.
Answer: 400×50=20 000, so 2 029.8 is unreasonable.
Hint: Round both factors before multiplying.
Why: Compatible numbers reveal an order-of-magnitude error.
7. A length rounds to 6.2 cm to the nearest 0.1 cm. State its interval.
Answer: 6.15 cm ≤ length < 6.25 cm.
Hint: Move 0.05 below and above 6.2.
Why: Half a tenth gives the rounding boundaries.
8. Three prices are $18.95, $7.80 and $12.40. Estimate the total, then calculate it.
Answer: Estimate $19+$8+$12=$39; exact total $39.15.
Hint: Round each price to dollars first.
Why: The close estimate supports the exact sum.
9. A 12.48 m board is cut into 7 equal pieces. Estimate and calculate each length to the nearest centimetre.
Answer: Estimate 12.6÷7=1.8 m; exact 12.48÷7≈1.783 m, which is 178 cm to the nearest centimetre.
Hint: Divide in metres, convert to centimetres, then round to the nearest centimetre.
Why: The requested nearest-centimetre accuracy controls the final rounding.
10. A distance is reported as 8.4 km correct to the nearest 0.1 km. Give the interval of possible actual distances and decide whether 8.46 km could have produced the report.
Answer: The actual distance satisfies 8.35 ≤ d < 8.45 km. Therefore 8.46 km could not round to 8.4 km to the nearest 0.1 km.
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 | AC9M7N05 — round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions |
| 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 Round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions. |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions. |
| 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 Round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions. |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions. |
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:
Math Antics — Review rounding to a chosen place and use it to assess a calculated answer.
As you watch: Which digit decides whether the chosen place rounds up?
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Try it: Round 18.746 to one and two decimal places, then explain which precision would suit a length measurement.
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Mapped skill: round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions
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 | AC9M7N05 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N05 · 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: AC9M7N05 — Rounding, Accuracy and Reasonableness
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