lesson
Rounding and truncation create different intervals
1 · Learn
Rounding to one decimal place chooses the nearest tenth. A displayed 2.3 then represents 2.25≤x<2.35 under the usual half-up convention. Truncating to one decimal place cuts off later digits instead, so a positive displayed 2.3 represents 2.3≤x<2.4.
The lower endpoint is included in both examples and the upper endpoint is excluded. For negative values, reason on the number line rather than copying a positive rule blindly.
Limits of accuracy affect calculations. For positive lengths, an upper bound for a product uses upper endpoints. State whether an endpoint is attainable and do not round bounds again before using them.
2 · Worked example
A positive length shown as 7.2 cm: rounded to 0.1 cm gives 7.15≤L<7.25; truncated to 0.1 cm gives 7.2≤L<7.3.
3 · Your turn
Give the interval for positive x displayed as 4.6 after truncation to one decimal place. Compare it with rounding to one decimal place.
Check your answer
Truncated: 4.6≤x<4.7. Rounded: 4.55≤x<4.65.
4 · Apply your learning
Draw both intervals on one number line and test values just below, at and just above every boundary.
Adult guidance and safety
This is England national-curriculum core teaching, not an exam-board specification. Check prerequisite understanding, require clear working and use additional varied practice before judging fluency.
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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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