The scale of a map is given as 1:30000000. Two cities are 4 cm apart on the map. Find the actual distance between them:

Question

Accepted Answer

To determine the actual distance between the two cities based on the map scale, we need to use the given scale of 1:30,000,000. This means that 1 cm on the map represents 30,000,000 cm in reality.

The cities are 4 cm apart on the map. To find the actual distance, we multiply the distance on the map by the scale factor:

$$ \text{Actual distance} = 4 \, \text{cm} \times 30,000,000 $$

$$ \text{Actual distance} = 120,000,000 \, \text{cm} $$

To convert this distance from centimeters to kilometers, we use the conversion factor that 1 kilometer equals 100,000 centimeters:

$$ \text{Actual distance in km} = \frac{120,000,000 \, \text{cm}}{100,000} $$

$$ \text{Actual distance in km} = 1,200 \, \text{km} $$

Now, let's express this distance in scientific notation:

$$ 1,200 \, \text{km} = 12 \times 10^2 \, \text{km} $$

Therefore, the correct answer is Option 1: 12 × 10² km.

**Explanation for why other options are incorrect:**

- **Option 2: 12 × 10³ km** - This would imply an actual distance of 12,000 km, which is ten times greater than the calculated distance of 1,200 km. Therefore, this option is incorrect.

- **Option 3: 12 × 10⁵ km** - This would imply an actual distance of 1,200,000 km, which is vastly greater than the calculated distance. This option is incorrect.

- **Option 4: 12 × 10⁷ km** - This would imply an actual distance of 1,200,000,000 km, which is astronomically larger than the calculated distance. This option is incorrect.

In conclusion, the correct answer is Option 1: 12 × 10² km, as it accurately represents the actual distance between the two cities based on the given map scale.