Problem 108 - Chemistry Matter and Change

Question

Convert each mass measurement to its equivalent in kilograms. (Chapter 2) a. 247 \(\mathrm{g}\) \(\quad\) c. 7.23 \(\mathrm{mg}\) b. 53 \(\mathrm{mg}\) \(\quad\) d. 975 \(\mathrm{mg}\)

Step-by-Step Solution

Answer

a. 0.247 kg, b. 0.000053 kg, c. 0.00000723 kg, d. 0.000975 kg.

Step 1: Convert Grams to Kilograms

To convert from grams to kilograms, remember that 1 kilogram (kg) is equal to 1000 grams (g). Therefore, to convert a mass measured in grams to kilograms, divide the number of grams by 1000. For example, for part (a), the conversion is:\[247 \, \mathrm{g} = \frac{247}{1000} \, \mathrm{kg} = 0.247 \, \mathrm{kg}\]

Step 2: Convert Milligrams to Kilograms

Since 1 kilogram equals 1,000,000 milligrams (mg), converting milligrams to kilograms involves dividing the mass in milligrams by 1,000,000.For part (b) (53 mg):\[53 \, \mathrm{mg} = \frac{53}{1,000,000} \, \mathrm{kg} = 0.000053 \, \mathrm{kg}\]For part (c) (7.23 mg):\[7.23 \, \mathrm{mg} = \frac{7.23}{1,000,000} \, \mathrm{kg} = 0.00000723 \, \mathrm{kg}\]For part (d) (975 mg):\[975 \, \mathrm{mg} = \frac{975}{1,000,000} \, \mathrm{kg} = 0.000975 \, \mathrm{kg}\]

Key Concepts

Understanding Grams to Kilograms Conversion

The conversion from grams to kilograms is a straightforward process. Grams and kilograms are both units of mass within the metric system, where kilograms are a larger unit. The key principle to remember is that 1 kilogram (kg) is equal to 1000 grams (g). This means for any given mass in grams, you can convert it to kilograms by dividing by 1000. For example, if you have 247 grams, you calculate the conversion by:\[247 \, \text{g} = \frac{247}{1000} \, \text{kg} = 0.247 \, \text{kg}\]This approach, dividing by 1000, works universally for any mass expressed in grams, regardless of its size. If you have 5000 grams, simply divide by 1000 to find out it's 5 kilograms. This conversion is crucial for scientific and everyday calculations that require mass measurements in kilograms, the base unit for mass in the metric system.

Converting Milligrams to Kilograms

Milligrams are an even smaller unit of mass in the metric system compared to grams. To convert milligrams to kilograms, it's important to recognize the relationship between these units. 1 kilogram is equivalent to 1,000,000 milligrams. Thus, to convert any mass from milligrams to kilograms, you divide the number of milligrams by 1,000,000. Take, for instance, 53 milligrams. When converted to kilograms, it becomes:\[53 \, \text{mg} = \frac{53}{1,000,000} \, \text{kg} = 0.000053 \, \text{kg}\]Let's consider another example with 975 milligrams. The conversion would be:\[975 \, \text{mg} = \frac{975}{1,000,000} \, \text{kg} = 0.000975 \, \text{kg}\]These calculations illustrate how even very small quantities in milligrams need careful conversion into kilograms for precise and meaningful results in scientific contexts.

Exploring Metric System Conversions

The metric system is a decimal-based system of measurement used around the world, and understanding its conversion is vital. It operates on a scale of 10, making conversions within the system particularly simple.

• Kilograms (kg) - the base unit for mass in the metric system, often used for heavier weights.
• Grams (g) - used for measuring smaller quantities than kilograms. There are 1000 grams in a kilogram.
• Milligrams (mg) - for even smaller quantities, where 1 gram equals 1000 milligrams. As such, there are 1,000,000 milligrams in a kilogram.

When converting metric system units, you usually work by simple division or multiplication by 10, or a power of 10. This regular pattern of scale makes it very practical for everyday use as well as in scientific fields. Mastery of these conversions allows for seamless transitions between units, crucial for accurate scientific calculations, cooking measurements, and various other applications.