Problem 44 - Fundamentals of Mathematics

Question

Convert \(463 \mathrm{mg}\) to \(\mathrm{cg}\).

Step-by-Step Solution

Answer

463 mg is equal to 46.3 cg.

Step 1: Identify the Units

We need to convert milligrams (mg) to centigrams (cg). This requires understanding the metric system relationship between these two units.

Step 2: Understand the Conversion Relationship

In the metric system, 1 gram is equal to 1000 milligrams and also equal to 100 centigrams. Therefore, 1 milligram is 0.1 centigrams since we divide by 10 when converting from milligrams to centigrams.

Step 3: Set Up the Conversion

To convert a mass from milligrams to centigrams, we use the factor 0.1. This means we multiply the number of milligrams by 0.1 to get the equivalent in centigrams. In this case, we have 463 mg.

Step 4: Perform the Calculation

Multiply the given milligrams by the conversion factor. Calculate:\[ 463 \, \text{mg} \times 0.1 = 46.3 \, \text{cg} \]

Step 5: Verify the Result

Double-check the multiplication to ensure accuracy: - Take 463 - Multiply by 0.1, shift the decimal point one place to the left results in 46.3. The conversion is verified.

Key Concepts

Milligrams to Centigrams Conversion

Converting milligrams ( mg ) to centigrams ( cg ) is a common task when dealing with metric units of mass. The metric system is based on powers of ten, making these conversions simpler. Here's how you can easily convert from milligrams to centigrams:

• First, understand that 1 gram ( g ) consists of 1000 milligrams (as it's a smaller unit) and also comprises 100 centigrams (since centigram is slightly larger compared to milligrams).
• This tells us that to move from milligrams to centigrams, we need to convert downward in scale, simply requiring division by 10.
• Thus, the conversion factor for 1 mg to cg is 0.1 , indicating a straightforward conversion.

In practical terms, when you are given a quantity in milligrams and need it in centigrams, you multiply the number of milligrams by 0.1 . This operation shifts the decimal point one place to the left. For instance, converting 463 mg results in 46.3 cg as calculated using this factor.

Understanding Metric Units

The metric system, also known as the International System of Units (SI), is a comprehensive and universally accepted system of measurements. Its main feature is the decimal basis, which is simple and straightforward, facilitating conversions as needed:

• All units are based on powers of ten, ensuring that scaling up or down by a factor of ten is consistent and easy to perform with simple multiplication or division.
• Units such as meter, gram, and liter are its fundamental units for length, mass, and volume, respectively.
• Prefixes like milli-, centi-, and kilo- denote fractions and multiples of these base units, enhancing versatility.

For students learning metric conversions, remembering key relationships can be helpful, such as 1 gram = 1000 mg and 1 gram = 100 cg . Emphasizing the simplicity of moving decimal places when scaling up or down makes transitioning between different units approachable.

Mathematical Calculations in Metric System

Performing calculations within the metric system involve basic mathematical operations, primarily addition, subtraction, multiplication, and division. The importance of these simple operations highlights the metric system's ease of use:

• When converting between units, multiplication or division is typically used to apply the conversion factor.
• To convert from a smaller unit to a larger unit (like milligrams to centigrams), multiply by the appropriate conversion factor (e.g., multiply by 0.1 ).
• Conversely, converting from a larger unit to a smaller one involves division (like converting centigrams to milligrams, where you would multiply by 10).

For the conversion of 463 mg to 46.3 cg , the calculation process is simple: multiply the initial value in milligrams by the conversion factor 0.1 . By shifting the decimal point one place to the left, we quickly arrive at the correct answer. Overall, recognizing and applying these small yet systematic actions makes working with metric units efficient and precise.