Question

Convert the following to the equivalent measures indicated. \(4 \mathrm{~g}=\) ______ \(\mathrm{mg}\)

Short answer

4 grams is equal to 4000 milligrams.

Step-by-step solution

Understand the Relationship

Recall the conversion factor between grams and milligrams. We know that 1 gram (g) is equivalent to 1000 milligrams (mg). This means for every gram, there are 1000 milligrams.

Set Up the Conversion Equation

Using the conversion factor, set up an equation. To convert grams to milligrams you multiply the number of grams by 1000 to find out how many milligrams there are.

Perform the Calculation

Multiply 4 grams by 1000 milligrams per gram to convert. \[ 4 ext{ g} imes 1000 ext{ mg/g} = 4000 ext{ mg} \]

Write the Answer

Write down the final answer from the calculation performed in Step 3.

Key concepts

Grams to Milligrams

Converting grams to milligrams is a simple yet essential skill in metric conversions. The metric system uses powers of ten, making its conversions straightforward and standardized.
Grams and milligrams are both units used to measure mass. - **Gram (g)**: A basic unit for measuring mass in the metric system. - **Milligram (mg)**: A smaller unit, which is one-thousandth of a gram. To convert grams to milligrams, you apply the principle that 1 gram equals 1000 milligrams. This conversion reflects the nature of the metric system and its base-10 structure, which makes switching between units a straightforward process. For example, to convert 4 grams to milligrams, you multiply 4 by 1000, resulting in 4000 milligrams.

Conversion Factors

Conversion factors are crucial tools in the realm of measurement conversion. They act as a bridge, allowing you to switch from one unit to another. A conversion factor is simply a ratio expressing how many of one unit are equal to another unit.
A key point to remember about conversion factors: - They are based on a known relationship between two units. For instance, the conversion factor between grams and milligrams is 1000 milligrams per gram. - They always equal one in value, meaning the quantity doesn't change, only the units do. To use a conversion factor to convert grams to milligrams, multiply the number of grams by the conversion factor, which, in this case, is 1000 mg/g. This multiplication process is known as dimensional analysis, and it's a fundamental technique in physics, chemistry, and everyday applications.

Measurement Conversion

Measurement conversion involves changing a quantity expressed in one unit into a different unit without altering its value. It's a vital skill across science, cooking, engineering, and more.
The metric system simplifies this process since it is decimal-based: - Identify the units involved. In this case, we're converting from grams to milligrams. - Use the appropriate conversion factor. Here, 1 gram equals 1000 milligrams. The process for conversion: 1. Determine the starting quantity in grams. 2. Apply the conversion factor by multiplying the grams by 1000. 3. State the new measurement in milligrams. Understanding measurement conversion not only helps in accurately calculating quantities but also reinforces comprehension of the relationship between different units within the same measurement system. This skill ensures precision and accuracy in a wide range of practical and academic tasks.