Scale Drawings and Measurement Bounds

Section 1What a scale drawing is

A scale drawing is an accurate drawing where every length has been enlarged or reduced by the same scale factor. The shape stays in proportion, but the size changes. In plain words, a school plan, house plan, or map is useful because the distances shrink in a controlled way.

Section 2Map scales

A map scale tells you how map distance compares with real distance. A scale of 1:50000 means 1 unit on the map represents 50000 of the same units in real life. Watch out: both sides of a ratio scale use the same unit before conversion.

Section 3Using line scales

A line scale is a drawn scale bar that shows real distances directly. Measure the map length, compare it with the scale bar, then convert to the real distance. This is common with Caribbean maps, where towns may be only a few centimetres apart on paper but many kilometres apart in real life.

Section 4Scale factors

To find real length from drawing length, multiply by the scale factor. To find drawing length from real length, divide by the scale factor. Easy to mix up - if a drawing is smaller than real life, the real length should be bigger than the drawing length.

Section 5Maximum and minimum measurements

A rounded measurement is not exact. If a length is 8 cm to the nearest cm, the true length is at least 7.5 cm and less than 8.5 cm. The minimum is the lower bound, and the maximum is the upper bound.

Section 6Margin of error

The margin of error is the greatest possible difference between the rounded measurement and the true value. When rounding to the nearest unit, the margin of error is half of that unit. So a mass measured to the nearest kilogram has a margin of error of 0.5 kg.

Section 7Bounds in calculations

For calculations using measured values, choose bounds carefully. The maximum possible sum uses upper bounds, and the minimum possible sum uses lower bounds. For a difference, the maximum possible difference uses the first upper bound minus the second lower bound.