Question

Perform each unit conversion. a. 27.8 \(\mathrm{L}\) to \(\mathrm{cm}^{3} \quad\) b. 1898 \(\mathrm{mg}\) to \(\mathrm{kg} \quad\) c. 198 \(\mathrm{km}\) to \(\mathrm{cm}\)

Short answer

a. 27,800 \( \mathrm{cm}^3 \) b. 0.001898 \( \mathrm{kg} \) c. 19,800,000 \( \mathrm{cm} \)

Step-by-step solution

Convert Liters to Cubic Centimeters

To convert liters to cubic centimeters, use the fact that 1 liter is equal to 1,000 cubic centimeters. Multiply the volume in liters by 1,000 to find the volume in cubic centimeters.

Convert Milligrams to Kilograms

To convert milligrams to kilograms, use the fact that 1 kilogram is equal to 1,000,000 milligrams. Divide the mass in milligrams by 1,000,000 to find the mass in kilograms.

Convert Kilometers to Centimeters

To convert kilometers to centimeters, use the fact that 1 kilometer is equal to 100,000 centimeters. Multiply the distance in kilometers by 100,000 to find the distance in centimeters.

Key concepts

Volume Conversion

Understanding volume conversion is essential for a variety of scientific calculations. Let's consider the exercise where we convert from liters to cubic centimeters (cm³). This process typically involves a clear recognition of the relationship between the two units. Since 1 liter is the same as 1,000 cm³, to convert liters to cubic centimeters, you simply multiply the volume in liters by 1,000.

For instance, to convert 27.8 liters to cubic centimeters, the calculation would look like this: \[ 27.8 \, \text{L} \times 1,000 = 27,800 \, \text{cm}^3 \].
This simple multiplication gives you the volume in cubic centimeters. It's important to know these basic unit conversions, as they lay the foundation for understanding more complex chemical measurements.

Mass Conversion

Another key concept in chemistry is mass conversion. The exercise presented involves changing milligrams (mg) to kilograms (kg), which introduces the scale difference between mass units. Because 1 kg equals 1,000,000 mg, converting from a smaller unit (mg) to a larger unit (kg) requires a division.

Here's how you would convert 1898 milligrams to kilograms: \[ \frac{1898 \, \text{mg}}{1,000,000} = 0.001898 \, \text{kg} \].
Remembering that the conversion factor between mg and kg is 1 million is crucial. Creating a step-by-step approach by recognizing the correct conversion factor simplifies the process and ensures accuracy in your measurements.

Length Conversion

When dealing with length conversion, it's about understanding the relationship between different units of length, such as kilometers and centimeters. In our exercise, we're asked to convert kilometers to centimeters. Since 1 km is equivalent to 100,000 cm, you'll need to multiply to convert from a larger unit (km) to a smaller unit (cm).

For a practical example: \[ 198 \, \text{km} \times 100,000 = 19,800,000 \, \text{cm} \].
Being comfortable with converting between units of length is vital, not only in chemistry but also in everyday situations such as measuring distances for travel.

Metric System

The metric system is a standardized system of measurement used in science, including chemistry. It is based on multiples of ten, making unit conversions more straightforward than those in other systems. Understanding the prefixes, such as 'milli-' for thousandths, 'centi-' for hundredths, 'kilo-' for thousands, etc., is fundamental.

In our exercise solutions, each step relies on the metric system's base conversions: