10.2 Ratios in Maps

Have you spotted that most maps print a ratio, often tucked into the lower-right corner, something like 1 : 75{,}00{,}000? That ratio is the map’s scale, and it carries a lot of information.

Representative Fraction (RF) A Representative Fraction (RF) is the ratio between a distance measured on the map and the matching real distance on the ground. An RF of 1 : 75{,}00{,}000 tells us that 1 cm on the map corresponds to 75,00,000 cm on the ground.

To make this feel concrete, let us convert the ground distance into kilometres. Since there are 100 cm in a metre and 1000 metres in a kilometre, 1 km = 100 \times 1000 = 1{,}00{,}000 cm. Hence

75{,}00{,}000 \text{ cm} = \frac{75{,}00{,}000}{1{,}00{,}000} \text{ km} = 75 \text{ km}.

So on this map, 1 cm stands for 75 km of geographical distance. (Keep in mind: this is the straight-line geographical distance, not the twisting road distance!)

Try This Open an atlas and use a ruler to measure the map distance between two cities you care about, say Pune and Hyderabad. Multiply by the map’s scale to estimate the geographical distance. Then locate the same pair of cities on a different map with a different scale. Do the two maps give roughly equal ground distances? They ought to, the land itself never changes, only the size of the drawing!

Scale in the Real World A small-scale map (like 1 : 1{,}00{,}00{,}000) shows a huge area, a whole country, but with little detail. A large-scale map (like 1 : 5{,}000, used for a town plan) covers a tiny area but shows streets and buildings clearly. Counter-intuitively, the bigger the second number in the RF, the smaller the scale. Architects, surveyors and the Survey of India all rely on RF scales every day.

Worked Example

On a map with RF 1 : 40{,}00{,}000, two towns sit 6 cm apart. What is the ground distance?

Here 1 cm represents 40{,}00{,}000 cm = 40 km. So 6 cm represents 6 \times 40 = 240 \text{ km}.

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