Year 7 Mathematics · AC9M7N05

Rounding, Accuracy and Reasonableness

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

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Learning goalsSay it simply

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.

Success criteria

  • I can round decimals to decimal-place or significant-figure accuracy.
  • I can select and justify an accuracy appropriate to a context.
  • I can use estimation and bounds to check whether a solution is reasonable.
Key conceptTeach from the board

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

Round to a stated accuracy

  1. Use 47.386.
  2. For two decimal places, inspect the third decimal digit, 6.
  3. Increase the hundredths digit from 8 to 9.
  4. Write 47.39.

Final answer: 47.386 rounds to 47.39 to two decimal places.

Check: The error 0.004 is less than 0.005.

Example 2

Estimate to check reasonableness

  1. Estimate 48.7 as 50.
  2. Estimate 19.8 as 20.
  3. Multiply 50×20=1000.
  4. Reject 96.426 as unreasonable for 48.7×19.8.

Final answer: The product should be about 1000, not 96.426.

Check: The exact product 964.26 is close to the estimate.

Example 3

Application problem 1

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.

  1. Plan: Represent the information first, then calculate, interpret and independently check the result.
  2. Work: 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.
  3. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

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

Application problem 2

Problem: A 12.48 m board is cut into 7 equal pieces. Estimate and calculate each length to the nearest centimetre.

  1. Plan: Divide in metres, convert to centimetres, then round to the nearest centimetre.
  2. Work: Estimate 12.6÷7=1.8 m; exact 12.48÷7≈1.783 m, which is 178 cm to the nearest centimetre.
  3. Interpret: The requested nearest-centimetre accuracy controls the final rounding.

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M7N05 - Rounding, Accuracy and Reasonableness
Example 1

Example 1 Round to a stated accuracy Use 47.386. For two decimal places, inspect the third decimal digit, 6. Increase the hundredths digit from 8 to 9. Write 47.39. Final answer: 47.386 rounds to 47.39 to two decimal places. Check: The error 0.004 is less than 0.005.

Example 2

Example 2 Estimate to check reasonableness Estimate 48.7 as 50. Estimate 19.8 as 20. Multiply 50×20=1000. Reject 96.426 as unreasonable for 48.7×19.8. Final answer: The product should be about 1000, not 96.426. Check: The exact product 964.26 is close to the estimate.

Example 3

Example 3 Application problem 1 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. Plan: Represent the information first, then calculate, interpret and independently check the result. Work: The actual distance satisfies 8.35 ≤ d &lt; 8.45 km. Therefore 8.46 km could not round to 8.4 km to the nearest 0.1 km. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills. Final answer: The actual distance satisfies 8.35 ≤ d &lt; 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

Example 4 Application problem 2 Problem: A 12.48 m board is cut into 7 equal pieces. Estimate and calculate each length to the nearest centimetre. Plan: Divide in metres, convert to centimetres, then round to the nearest centimetre. Work: Estimate 12.6÷7=1.8 m; exact 12.48÷7≈1.783 m, which is 178 cm to the nearest centimetre. Interpret: The requested nearest-centimetre accuracy controls the final rounding. 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.

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions
  • E1: identifying the interval between a pair of consecutive integers that includes a given rational number
  • E2: choosing and applying conventions for rounding correct to a specified number of decimal places based upon the context
  • E3: checking that the accuracy of rounding is suitable for context and purpose, such as the amount of paint required and cost estimate for renovating a house; for example, purchasing 2 litres of paint to paint the bedroom even though 1.89 litres is the exact answer or estimating a renovation budget to the nearest \$100
Questions and answersWith answers

Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.

  1. 1. Round 8.746 to one decimal place.

    Check answer

    Answer: 8.7.

    Hint: Inspect the digit immediately to the right.

    Why: The hundredths digit 4 does not round the tenths up.

  2. 2. Round 3 482 to the nearest hundred.

    Check answer

    Answer: 3 500.

    Hint: Mark the hundreds digit first.

    Why: The tens digit 8 rounds the hundreds up.

  3. 3. Round 0.006784 to two significant figures.

    Check answer

    Answer: 0.0068.

    Hint: Count from 6, not from the decimal point.

    Why: Significant figures begin at the first non-zero digit.

  4. 4. A journey is 186.7 km. Give a sensible whole-kilometre report.

    Check answer

    Answer: 187 km.

    Hint: Round to the nearest kilometre.

    Why: Whole kilometres suit a general travel-distance report.

  5. 5. A medicine dose is 2.46 mL and must be measured to 0.1 mL. State the dose.

    Check answer

    Answer: 2.5 mL.

    Hint: Round to one decimal place.

    Why: The stated measuring precision determines rounding.

  6. 6. Estimate 398×51 and use it to check a reported answer of 2 029.8.

    Check answer

    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. 7. A length rounds to 6.2 cm to the nearest 0.1 cm. State its interval.

    Check answer

    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. 8. Three prices are $18.95, $7.80 and $12.40. Estimate the total, then calculate it.

    Check answer

    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. 9. A 12.48 m board is cut into 7 equal pieces. Estimate and calculate each length to the nearest centimetre.

    Check answer

    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. 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.

    Check answer

    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.

Practice and reviewReady for practice

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.

Curriculum alignmentStart here

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.

Success criteria

  • I can round decimals to decimal-place or significant-figure accuracy.
  • I can select and justify an accuracy appropriate to a context.
  • I can use estimation and bounds to check whether a solution is reasonable.
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