Convert the following 75 km to dm, cm and dam.
The Correct Answer and Explanation is:
Conversion of 75 kilometers:
- To decameters (dam):
75 km = 7,500 dam - To decimeters (dm):
75 km = 750,000 dm - To centimeters (cm):
75 km = 7,500,000 cm
Explanation
Unit conversion in the metric system is a process that involves multiplying or dividing by powers of ten. The metric system is based on the decimal system, making it easy to convert between units by simply moving the decimal point. In this case, we are converting 75 kilometers to three different units: decameters, decimeters, and centimeters.
To begin, understand the base relationships between these units and the meter. A kilometer is equal to 1,000 meters. A decameter is equal to 10 meters, a decimeter is equal to 0.1 meters, and a centimeter is equal to 0.01 meters. Using these relationships, we can calculate the equivalent values in each unit.
First, we convert kilometers to decameters. Since 1 kilometer is equal to 100 decameters, we multiply 75 by 100. The result is 7,500 decameters.
Next, we convert kilometers to decimeters. Since 1 kilometer equals 10,000 decimeters (because 1 km = 1,000 meters and 1 m = 10 dm), we multiply 75 by 10,000. This gives us 750,000 decimeters.
For centimeters, we use the fact that 1 kilometer equals 100,000 centimeters. This is because 1 meter equals 100 centimeters and 1 kilometer equals 1,000 meters, so 1,000 multiplied by 100 equals 100,000. Multiplying 75 by 100,000 results in 7,500,000 centimeters.
Understanding how these units relate to each other helps in everyday applications such as measuring distances on maps, constructing buildings, or working in scientific fields. The simplicity of multiplying and dividing by powers of ten makes the metric system efficient and widely adopted around the world.
