Measurements, rounding and reported precision
Report a measurement at a justified precision and separate a rounded estimate from a decision about whole items.
What you will tackle
- Interpret nearest-unit measurements as intervals
- Round arithmetic and statistical results appropriately
- Estimate lengths using a scale
- Distinguish measurement uncertainty from integer purchasing constraints
A recorded value has a resolution
A positive length recorded as 12 cm to the nearest centimetre represents values from 11.5 cm up to but not including 12.5 cm under the usual half-up convention. Extra calculator digits do not improve the measuring instrument. Keep guard digits during calculations and round the final reported result to the precision requested.
Estimates and decisions
Use a known scale length to estimate another segment only when the diagram is stated to be to scale. A reported mean may need rounding; the unrounded mean still determines the arithmetic. By contrast, the number of boxes needed to hold objects requires rounding up, while the number affordable under a budget requires rounding down.
Build your notes, then practise
Work on paper before opening an explanation. Guided tasks provide a starting point; independent tasks remove the scaffolding; application tasks ask you to justify a method or interpretation in context.
Guided practice
Guided 1
A length is recorded as 8.4 cm to the nearest 0.1 cm. Give its possible interval. Find the mean of 7.2, 7.5 and 7.9 cm, reporting to one decimal place.
Show a starting hint
Use half the rounding increment on either side.
Compare with the explained answer
- Half a 0.1 cm step is 0.05 cm, so the interval is 8.35 ≤ L < 8.45.
- The unrounded mean is 22.6/3 = 7.5333… cm.
- To one decimal place it is 7.5 cm; the trailing calculator digits are not additional measured precision.
Answer / response criteria: 8.35 ≤ L < 8.45 cm; mean 7.5 cm.
Independent practice
Independent 1
A rectangle is reported as 12 cm by 5 cm, each to the nearest centimetre. Give the possible area interval. Report 53/7 to two decimal places.
Compare with the explained answer
- The side intervals are 11.5 ≤ L < 12.5 and 4.5 ≤ W < 5.5.
- Both sides are positive, so minimum area is 11.5·4.5 = 51.75 and the upper bound is 12.5·5.5 = 68.75, excluded.
- 53/7 = 7.571428… rounds to 7.57.
Answer / response criteria: 51.75 ≤ A < 68.75 cm²; 7.57.
Application practice
Application 1
A scale drawing has a 4 cm segment representing 10 m. Another measured segment is 3.2 cm; estimate its real length. Then find boxes needed for 53 books at 7 per box and whole $7 tickets affordable with $53. Explain the three uses of rounding.
Compare with the explained answer
- The scale is 2.5 m per cm, giving an estimated 8 m, subject to drawing and measurement precision.
- 53/7 is about 7.57, so eight boxes are needed to hold all books.
- Only seven tickets can be bought; eight would cost $56. A spatial estimate, capacity ceiling and budget floor answer different questions.
Answer / response criteria: About 8 m; 8 boxes; 7 tickets.
What can you explain now?
A scale drawing has a 4 cm segment representing 10 m. Another measured segment is 3.2 cm; estimate its real length. Then find boxes needed for 53 books at 7 per box and whole $7 tickets affordable with $53. Explain the three uses of rounding.
Compare with the explanation
About 8 m; 8 boxes; 7 tickets.
Explain the reasoning before comparing. This review records your self-assessment rather than an official score or mastery decision.
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Source and review status
Coverage follows the named requirements and examples in the 2026–2027 ACT test guide and subject descriptions. That guide explicitly does not list every possible topic. The broader coded College and Career Readiness Standards are also mapped to conceptual teaching and practice; this does not calibrate a learner to a score band. The separate scientific-background context list and reading-complexity rubric have their own stated limits.
Original teaching and explained self-check practice are available. Specialist review and difficulty calibration remain pending. Essays require self-check or teacher review and are not automatically marked or awarded official scores.
Official source specification / guide