Question

question 1: convert verbal scale to ratio scale
convert the following verbal scales into a ratio scale (representative fraction).
a) 1 cm represents 1 km
b) 1 cm represents 500 km
c) 1 cm represents 5 km
d) 1 cm represents 230 km

question 2: convert ratio scale to verbal scale
convert the following ratio scales into a verbal scale (state how much distance on the ground is represented by 1 cm on the map).
a) 1 : 25,000
b) 1 : 100,000
c) 1 : 50,000
d) 1 : 250,000

Explanation:

Step1: Recall unit - conversion

1 km = 100000 cm.

Step2: Convert verbal scale to ratio scale for part a

If 1 cm represents 1 km, then the ratio scale is $\frac{1}{100000}$.

Step3: Convert verbal scale to ratio scale for part b

If 1 cm represents 500 km, since 500 km = 500×100000 = 50000000 cm, the ratio scale is $\frac{1}{50000000}$.

Step4: Convert verbal scale to ratio scale for part c

If 1 cm represents 5 km, since 5 km = 5×100000 = 500000 cm, the ratio scale is $\frac{1}{500000}$.

Step5: Convert verbal scale to ratio scale for part d

If 1 cm represents 230 km, since 230 km = 230×100000 = 23000000 cm, the ratio scale is $\frac{1}{23000000}$.

Step6: Convert ratio scale to verbal scale for part a

If the ratio scale is 1:25000, then 1 cm on the map represents 25000 cm on the ground. Since 25000 cm = 250 m (because 1 m = 100 cm), 1 cm on the map represents 250 m on the ground.

Step7: Convert ratio scale to verbal scale for part b

If the ratio scale is 1:100000, then 1 cm on the map represents 100000 cm on the ground. Since 100000 cm = 1 km, 1 cm on the map represents 1 km on the ground.

Step8: Convert ratio scale to verbal scale for part c

If the ratio scale is 1:50000, then 1 cm on the map represents 50000 cm on the ground. Since 50000 cm = 500 m, 1 cm on the map represents 500 m on the ground.

Step9: Convert ratio scale to verbal scale for part d

If the ratio scale is 1:250000, then 1 cm on the map represents 250000 cm on the ground. Since 250000 cm = 2.5 km, 1 cm on the map represents 2.5 km on the ground.

Answer:

Question 1:
a) $\frac{1}{100000}$
b) $\frac{1}{50000000}$
c) $\frac{1}{500000}$
d) $\frac{1}{23000000}$
Question 2:
a) 1 cm on the map represents 250 m on the ground
b) 1 cm on the map represents 1 km on the ground
c) 1 cm on the map represents 500 m on the ground
d) 1 cm on the map represents 2.5 km on the ground