lesson
A rounded value represents an interval
1 · Learn
If a positive length rounds to 8.4 cm to the nearest tenth, its original value is at least 8.35 cm and less than 8.45 cm under the usual halfway-up convention. The displayed value is not an exact measurement of every possible original.
State the rounding unit and endpoint convention. A calculation using rounded measurements may have uncertainty; extra calculator digits do not restore information that was never measured.
2 · Worked example
A value of 8.349 rounds to 8.3, while 8.35 rounds to 8.4. A value of 8.45 rounds to 8.5, explaining the different endpoint signs.
3 · Your turn
Give the interval for a positive mass recorded as 12 kg to the nearest kilogram.
Check your answer
11.5 kg <= mass < 12.5 kg under the stated convention.
4 · Apply your learning
Place boundary examples on a number line and explain why rounded measurements should not be described as exact.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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