3.3.2 Scale

3.3.2 Scale

Scale refers to the relationship between the size of an object or distance on a map or drawing and the corresponding size of the object or distance in the real world. In other words, scale is the ratio of the size of the object or distance on the map to the size of the object or distance in real life.

• Maps and architectural or engineering drawings are commonly drawn to scale so that they can accurately represent real-world features and dimensions.
• For example, a map may have a scale of \( 1 \) : \( 50000\) meaning that one unit of measurement on the map (such as an inch) represents \( 50000 \) units of measurement in the real world (such as feet or meters).
• Scale is often expressed as a ratio or a fraction, such as \( 1 \) : \( 50000 \) or \( \frac{1}{50000} \) or as a graphic scale, which is a line or bar that shows the relationship between the map or drawing and the real world.
• Using scale is important for accurately representing real-world features and dimensions on maps and drawings, and for making measurements and calculations based on those representations.

Use of scale to convert lengths:

Scale can be used to convert lengths between the map or drawing and the real world. To convert a length on a map or drawing to the corresponding length in the real world, you can use the scale factor or ratio.

• For example, if the scale of a map is \( 1 \) : \( 50000 \) and you want to convert a distance of \( 2 \) inches on the map to the real-world distance, you would use the following formula:

\( Real \ world \ distance \ = Map \ distance \times \ Scale \ factor \)

• The scale factor in this case is \( 50000 \) so the calculation would be:

\( Real \ world \ distance \ = 2 \ inches \times 50000 \ = \ 100000 \ inches \)

• To convert this to a more practical unit of measurement, you could divide by \( 12 \) to get the distance in feet:

\( Real \ world \ distance \ =\frac{100000 \ inches}{12} =8333.33 \ ft \)

• Conversely, to convert a real-world distance to the corresponding distance on a map, you would use the inverse formula:

\( Map \ distance = \frac{Real \ world \ distance}{Scale \ factor} \)

• For example, if the real-world distance between two points is \( 1 \) mile, or \( 5280 feet \), and the map scale is \( 1 \) : \( 50000 \) the map distance would be:

\( Map \ distance \ =\frac{5280 \ ft}{50000} = 0.1056 \ inches \)

• Using scale to convert lengths is a useful tool for making measurements and calculations based on maps and drawings, and for accurately representing real-world features and dimensions.