Converting Units

Mastering Unit Conversion in the Metric System

The metric system is a fundamental tool for measuring physical quantities, and understanding the conversion of units within it is crucial for accuracy. Each metric unit is a combination of a base unit and a prefix, with each succeeding unit being 10 times larger than the previous one. Let's explore some examples to better comprehend this concept.

5 kilograms
In this case, the base unit is grams and the prefix is kilo. Consulting the table, we can determine that 1 kilogram equals 1000 grams, making 5 kilograms equivalent to 5000 grams.
The symbols for grams and kilo are g and k respectively, and can also be written as 5 kg.
Using the table, can you convert 5 kg to centigrams?
Based on the table, kilo is represented as 10³ and centi as 10^-2. Therefore, converting 5 kg to centigrams results in 500,000 centigrams.

Now, let's consider a different scenario:

If we want to express 12 cm in hm, we know that cm stands for centimeters and hm stands for hectometers. Converting from cm to hm yields:

12 cm = 0.0012 hm

So far, we have only converted units with the same base units. Next, let's see how to convert derived units composed of multiple base units.

To refresh your knowledge on fundamental and derived quantities, refer to our article on physical quantities.

When converting units, it is essential to express the unit to be converted as a combination of its fundamental units. Then, replace each fundamental unit with its corresponding value in the desired unit and evaluate the obtained value and its magnitude to obtain the converted value.

Let's see this in action with an example:

Convert 8 m³ to cm³.

First, let's express m³ in terms of its fundamental units:
8 m³ = 8 m x m x m
Knowing that 1 m = 100 cm, we must convert m x m x m to cm x cm x cm.
Thus, 8 m³ = 8 x 100 cm x 100 cm x 100 cm
Evaluating the obtained value, we get:
8 x 100 x 100 x 100 cm³ = 8 x 10^6 cm³

As shown in the example above, 1 m³ is equivalent to 10^6 cm³. It is a common error to assume that 1 m³ equals 100 cm³, so take caution when converting cubic units.

Here's another example:

Convert 90 km/h to m/s.

First, let us express km/h in terms of its fundamental units:
90 km/h = 90 km x 1 h
Since 1 km = 1000 m and 1 h = 3600 s, we must convert km/h to m/s.
Consequently, 90 km/h = 90 x 1000 m x 1 h/3600 s
By evaluating the obtained value, we get:
90 x 1000 x 1/3600 m/s = 25 m/s

As seen in the above example, 1 km/h is equivalent to 5/18 m/s. This is a commonly used conversion value, and it can be utilized directly in exams without conversion.

Now, let's apply our knowledge to a real-life problem:

A car travels 108 km in 2 hours. What is its speed in m/s?

First, we know that 1 km/h = 5/18 m/s. Therefore, the speed of the car can be calculated as:
108 km / 2 hours = 54 km/h
Converting to m/s, we get: 54 km/h x 5/18 = 15 m/s

Key Takeaways:

When measuring physical quantities, it is critical to include both the magnitude and unit in your calculations.
There are various units available to express a measurement, so take care in selecting the appropriate one.
In the metric system, each unit is a combination of a base unit and a prefix, with each succeeding unit being 10 times larger than the previous one.
Remember to express the unit you want to convert in terms of its fundamental units, substitute those units with their corresponding values in the desired unit, and evaluate the obtained value to get the converted value.