19. Scale Drawing Precision and Measurement Error

Scale drawings are proportional, but measurements can still include rounding or small error.

If a map scale is 1 inch = 12 miles and a student measures 2.4 inches, the real distance is:
\[ 2.4(12)=28.8\text{ miles}. \]

If the measurement could be off by 0.1 inch, then the real distance could be off by:
\[ 0.1(12)=1.2\text{ miles}. \]
The scale factor magnifies the measurement error.

GED® questions may ask for the best estimate. If the map distance is about 3 inches and the scale is 1 inch = 9 miles, the real distance should be about 27 miles. An answer like 270 miles is probably a decimal or scale error.

When converting scale units, stay organized. If a blueprint uses 1 cm = 4 ft and a room measures 6.5 cm, then:
\[ 6.5(4)=26\text{ ft}. \]

Common misconception: treating scale drawings as exact even when the problem says "about" or gives rounded measurements.

Academic habit: after a scale calculation, compare your result to the measured drawing length. More drawing units should mean more real units.