Units, measurement and scale: clear practical guide

Geometry and measures • Mensuration and calculation

Flashcards

Test your knowledge with interactive flashcards

Convert 1500 metres to kilometres.

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1.5 km.

Key concepts

What you'll likely be quizzed about

Standard units and simple conversions

Length uses millimetres (mm), centimetres (cm), metres (m) and kilometres (km). Mass uses grams (g) and kilograms (kg). Capacity and smaller volumes use millilitres (ml) and litres (L); larger volumes use cubic metres (m³). Time uses seconds (s), minutes (min) and hours (h). Money uses currency units (e.g., pounds, pence). Conversion between units uses multiplication or division by the conversion factor; for example, 1 m = 100 cm so multiply metres by 100 to get centimetres.

Area and volume unit scaling

Area units follow from linear units squared: 1 m² = (100 cm)² = 10 000 cm². Volume units follow from linear units cubed: 1 m³ = (100 cm)³ = 1 000 000 cm³. Capacity links to volume with 1 litre = 1 000 cm³ (1 dm³) and 1 m³ = 1 000 L. Cause → effect: when linear measurements double, areas quadruple and volumes increase eightfold because area scales with the square and volume with the cube of the linear scale factor.

Measuring line segments and angles

Line segments require straight-edge measurement and a clear unit label. Angles use a protractor to read degrees from 0° to 180° for interior angles; full rotation equals 360°. Cause → effect: inaccurate placement of the protractor centre or misreading the scale produces systematic error in angle measures. Label angles with degrees and show working when combining or subtracting angles.

Scale drawings and map interpretation

A scale uses a ratio (1:n) or statement (1 cm : 2 km) to link drawing units to real units. Cause → effect: a larger scale denominator produces a smaller representation (more reduction); therefore distances measured on the drawing multiply by the scale factor to give real distances. Area conversion on scale drawings requires squaring the linear scale factor; e.g., scale 1:100 means a 1 cm² area on the drawing represents 10 000 cm² in reality.

Bearings and directional measurement

Bearings measure clockwise from true north and use three figures (000°–359°). Example: 090° indicates east and 180° indicates south. Cause → effect: rotating the reference direction changes the bearing; therefore consistent reference to north is essential. Bearings give unambiguous direction between two points when used with maps or coordinates.

Key notes

Important points to keep in mind

Always include unit labels with every measured or calculated quantity.

When converting linear units, apply the factor once; for area apply the square of the factor; for volume apply the cube of the factor.

Use 1 L = 1 000 cm³ and 1 m³ = 1 000 L for linking volume and capacity units.

Read protractors with the correct scale (inner or outer) according to angle orientation to avoid a 180° error.

Interpret map scales by converting drawing units to the same real units before calculation (convert cm to metres or kilometres as needed).

Express bearings as three digits (e.g., 005°, 090°, 270°) to avoid ambiguity.

Check for measurement error by re-measuring or using alternative methods (e.g., coordinate differences for bearings).

When a scale is given as 1:n and lengths are in cm on the drawing, convert to metres by multiplying by n then dividing by 100 where appropriate.