The RF of a map

The idea

The Representative Fraction (RF) of a map, written as a ratio 1 : n, shows the ratio between a distance on the map and the corresponding actual geographical (not road) distance on the ground.

What does 1 cm stand for?

Many maps print a ratio in the lower right corner, for example RF 1 : 60,00,000.

On this map, 1 cm stands for how far on the ground?

• 60 cm
• 60 km
• 600 km

Lay the ruler on the map

This map prints RF 1 : 60,00,000. Tap two towns: a ruler lies between them. Read the map distance, then follow the lines down to the ground distance. Then press the road button.

1 cm on the map is n cm on the ground

The Representative Fraction (RF) of a map, written as a ratio 1 : n, shows the ratio between a distance on the map and the corresponding actual geographical (not road) distance on the ground.

RF 1 : 60,00,000 means 1 cm on the map is 60,00,000 cm on the ground. To change cm into km: 100 cm = 1 m and 1000 m = 1 km, so 1 km = 1,00,000 cm. 60,00,000 ÷ 1,00,000 = 60, so 1 cm on this map is 60 km.

Two towns 5 cm apart on the map are 5 × 60,00,000 = 3,00,00,000 cm which is 5 × 60 = 300 km apart on the ground.

The RF gives the straight-line distance, the way a bird flies. A road bends, so the road is longer.

Notes

The Representative Fraction (RF) of a map, written as a ratio 1 : n, shows the ratio between a distance on the map and the corresponding actual geographical (not road) distance on the ground.

Check yourself

A map has RF 1 : 60,00,000. Two towns are 3 cm apart on the map. How many km apart are they on the ground?

Answer: 180 km

3 × 60,00,000 = 1,80,00,000 cm, and ÷ 1,00,000 gives 180 km. Or: 3 × 60 km = 180 km.

The map has RF 1 : 60,00,000. Read the ruler. How many km is it from P to R on the ground?

Answer: 360 km

P and R are 6 cm apart on the map. 6 × 60 km = 360 km.

Two towns are 5 cm apart on a map with RF 1 : 60,00,000, so the RF gives 300 km. The road between them is longer than 300 km. Is the map wrong?

On the ground, two towns are 150 km apart. On a map with RF 1 : 60,00,000, how many cm apart are they on the map?

Answer: 2.5 cm

1 cm is 60 km, so the map distance is 150 ÷ 60 = 2.5 cm. In cm: 1,50,00,000 ÷ 60,00,000 = 2.5.

• Yes. The RF should give the road distance.. The RF is about the straight-line (geographical) distance, not the road distance.
• Yes. 5 cm must stand for the road length.. The RF compares the map distance with the straight-line distance on the ground. Roads are not measured by it.
• No. The RF gives the straight-line distance, and a bending road is longer. — correct. Yes! Geographical distance is the straight line. A road bends, so it is longer than the RF distance.