When dealing with maps, understanding the scale is crucial for accurate measurements. This article will guide you through a practical example, demonstrating how to convert real-world distances to map distances using the scale 1:10,000,000. We will use the specific example of the distance between Madang and Lae, both towns located in Papua New Guinea, where the actual distance is 720 km. Let's break down the steps and explore how you can achieve the correct answer.

Understanding the Scale

The scale 1:10,000,000 means that 1 cm on the map corresponds to 10,000,000 cm in reality. This scale is widely used for large-scale maps, providing a useful overview of regions across significant distances.

Step-by-Step Conversion

Let's start with the actual distance between Madang and Lae, which is 720 km. First, we need to convert kilometers to centimeters, as the scale is given in centimeters.

Convert kilometers to meters: Convert meters to centimeters: Divide the total centimeters by the scale denominator (10,000,000):

1. Convert kilometers to meters:

720 km 720,000 meters

2. Convert meters to centimeters:

720,000 meters 720,000,000 centimeters

3. Divide the total centimeters by the scale denominator:

720,000,000 cm / 10,000,000 72 cm

Therefore, the distance between Madang and Lae on the map is 7.2 cm, or 72 mm (as 1 cm 10 mm).

Alternative Methods of Conversion

There are a few alternative methods to achieve the same result. Here are some additional ways to convert the distance.

Using Google for Instant Calculations

Google can quickly provide the answer, but it's essential to interpret the results accurately. Here’s a demonstration of how Google might round the answer:

720 km 72,000,000 cm 72,000,000 cm / 10,000,000 7.2 cm

In this case, Google rounds it down to 7.2 cm, which is the correct answer.

Using Simple Ratios

The conversion can also be done using a simple ratio:

1:10,000,000 X : 72,000,000

Solving for X:

X 72,000,000 / 10,000,000 7.2 cm

Thus, the map distance is 7.2 cm.

Conclusion

In conclusion, understanding the scale of a map and accurately converting distances between the real world and the map can be straightforward with the right approach. Whether you use direct calculation, Google, or simple ratios, the result is consistently 7.2 cm for the distance between Madang and Lae on a map with a scale of 1:10,000,000.