Question

Convert the following metric measures by moving the decimal. \(0.33 \mathrm{~g}=\) ______ \(\mathrm{mg}\)

Short answer

330 mg

Step-by-step solution

Understand the Conversion

To convert grams to milligrams, we need to understand that there are 1,000 milligrams in 1 gram. This means when converting grams to milligrams, we multiply the number of grams by 1,000.

Set Up the Conversion Calculation

Start with the known value in grams, which is 0.33 g. Set up the equation using the conversion factor:\[ 0.33 \, ext{grams} imes 1000 \, rac{milligrams}{gram} \]

Perform the Multiplication

Multiply the given grams by 1,000 to convert to milligrams:\[ 0.33 imes 1000 = 330 \, ext{milligrams} \]

Check the Decimal Movement

When multiplying by 1,000, the decimal point moves three spaces to the right, which confirms that 0.33 grams is equivalent to 330 milligrams.

Key concepts

Decimal Movement

In the realm of metric conversions, understanding decimal movement is a key skill. Decimal movement relates to how the decimal point shifts when you multiply or divide numbers by powers of ten. When you multiply by 1,000, you are effectively moving the decimal point three places to the right.
For example, when converting 0.33 grams to milligrams, a multiplication by 1,000 is needed since there are 1,000 milligrams in a gram. Starting with 0.33, moving the decimal three spaces to the right takes the decimal point beyond the original number itself. Thus, 0.33 becomes 330.
This intuitive movement of the decimal simplifies computations, saving you from manual multiplication every time. Remember:

• Multiplying by 1,000 moves the decimal three places right.
• Dividing by 1,000 would move the decimal three places left.

Mastering this concept can significantly ease the process of metric conversions.

Grams to Milligrams Conversion

Converting grams to milligrams is a common but crucial task in mathematics and science. One gram is equivalent to 1,000 milligrams. This knowledge becomes essential when you are tasked with converting measurements between these two units.
In practice, this conversion is performed by multiplying the number of grams by 1,000. The factor of 1,000 emerges from the relationship between grams and milligrams. Essentially, this conversion reflects the metric system's orderly structure, where each unit step in the metric hierarchy corresponds to a factor of ten.
For instance, consider 0.33 grams. To convert it to milligrams, multiply 0.33 by 1,000:
\[0.33 \times 1000 = 330\]\
This arithmetic confirms that 0.33 grams equals 330 milligrams. Such conversions are used frequently in cooking, chemistry, and other fields requiring precise measurements.

Measurement Conversion Steps

Conducting measurement conversions can be straightforward as long as you follow structured steps. These steps not only ensure accuracy but also enhance comprehension of the process.
Here's how you tackle a grams to milligrams conversion:

• **Understand Conversion Requirements**: Recognize that 1 gram equals 1,000 milligrams, setting the stage for using the right conversion factor.
• **Set Up the Conversion**: Begin with your known measurement (e.g., 0.33 grams). Prepare to multiply this by 1,000, your conversion factor.
• **Conduct the Calculation**: Multiply your grams by 1,000:
  \[0.33 \text{ grams} \times 1000 = 330 \text{ milligrams}\]
• **Verify Decimal Movement**: Checks on decimal shifting reinforce the conversion's accuracy. Ensure your decimal point moved as anticipated.

Refining your adherence to these steps enhances precision in metric conversions, supporting correctness in any context where such transformations are required.