lesson
Choose the conversion for the quantity
1 · Learn
A measurement is a number AND a unit. 1.25 km means 1250 m because each kilometre contains 1000 metres. A smaller unit needs more units to describe the same length. To reverse the conversion, divide by 1000. Likewise 2500 g is 2.5 kg, not 2500 kg.
Capacity can be recorded in litres or millilitres: 1 L = 1000 mL, so 3.2 L = 3200 mL. One cubic centimetre has the same volume as one millilitre. Always label the result; a bare number does not say which measurement you mean.
Time does not use a factor of 100 between hours and minutes. 1.75 hours = 1 hour + 0.75×60 minutes = 1 hour 45 minutes, or 105 minutes. In reverse, 2 hours 15 minutes = 2 + 15/60 = 2.25 hours. Writing 2.15 hours would mean 2 hours 9 minutes.
An area uses two dimensions. A square one metre wide and one metre high is 100 cm by 100 cm, so 1 m² = 10000 cm². Thus 0.35 m² = 3500 cm². Multiplying by 100 would change only one dimension.
Volume uses three dimensions: a one-metre cube is 100 cm by 100 cm by 100 cm, so 1 m³ = 1000000 cm³. Because 1000 cm³ is one litre, 1 m³ = 1000 L. Therefore 0.012 m³ is 12000 cm³ or 12 L. Check whether the question is about length, area, volume or time before choosing a factor.
2 · Worked example
Convert 0.48 m² and 0.025 m³. The area is 0.48×10000 = 4800 cm². The volume is 0.025×1000000 = 25000 cm³ = 25 L. These are different quantities, so the conversion factors are different.
3 · Your turn
Convert 2.25 km to metres, 450 g to kilograms, 1.5 hours to minutes, and 0.008 m³ to litres.
Check your answer
2250 m; 0.45 kg; 90 minutes; 8 L. In the time calculation, 0.5 hour means 30 minutes, not 50.
4 · Apply your learning
On the working pad or paper, draw a conversion arrow and its inverse for each practice value. Sketch a square labelled 1 m on both sides, then relabel both sides in centimetres to explain the area factor.
Adult guidance and safety
Use invented measurements. No weighing pupils or sharing personal measurements is required. Distinguish capacity from mass; litres cannot be converted to kilograms without a substance's density.
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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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