Question

Convert the following to the equivalent measures indicated. \(0.8 \mathrm{~g}=\) ______ \(\mathrm{mg}\)

Short answer

0.8 grams is equal to 800 milligrams.

Step-by-step solution

Understand the Conversion Factor

To convert grams to milligrams, we use the fact that 1 gram is equal to 1000 milligrams. This conversion factor will help us change grams into milligrams.

Set Up the Conversion Equation

Write out the conversion equation using the conversion factor. Since 1 gram equals 1000 milligrams, the equation will be: \[0.8 \, \text{g} \times \frac{1000 \, \text{mg}}{1 \, \text{g}}\] This equation sets us up to cancel out the grams and convert to milligrams.

Perform the Multiplication

Carry out the multiplication from the conversion equation. Multiply 0.8 by 1000:\[0.8 \, \text{g} \times 1000 \, \text{mg/g} = 800 \, \text{mg}\] This result tells us how many milligrams are equivalent to 0.8 grams.

Key concepts

Understanding Conversion Factors

When we talk about converting units from one to another, conversion factors play a crucial role. A conversion factor is a number used to change one set of units to another, by multiplying or dividing. In our example of converting grams to milligrams, the conversion factor is 1000 because 1 gram equals 1000 milligrams. This means for every 1 gram you have, you also have 1000 milligrams.

Conversion factors are essential because they allow us to scale a measurement up or down without changing its relative value. They are based on universally accepted standards, so they help ensure your conversion is accurate and reliable.

• They make unit conversions easy and straightforward.
• Keep in mind that these factors are derived from definitions.
• Always check the units to ensure you’re applying the factor in the right direction.

Writing Mathematical Equations for Unit Conversion

Mathematical equations are your roadmap for converting one unit to another. These equations rely on the conversion factor you choose. In our example, changing grams to milligrams, the equation looks like this: \[0.8 \, \text{g} \times \frac{1000 \, \text{mg}}{1 \, \text{g}}\]

The key part of the equation is the fraction \(\frac{1000 \, \text{mg}}{1 \, \text{g}}\), which is your conversion factor. It's placed so that the units you want to get rid of (grams, in this case) are positioned to cancel out.

This fraction reveals how many of the new unit (milligrams) are equivalent to one of the old unit (grams).

• Always make sure the units cancel correctly. The original unit should appear in the denominator to ensure it gets eliminated.
• Check your fractions and multiplication logic twice to avoid mistakes.

The Multiplication Process in Unit Conversion

Once you have your conversion equation set up, the next step is the multiplication process. Multiplication is straightforward, but it's pivotal in ensuring the unit conversion is accurate. From our example of converting 0.8 grams to milligrams, you multiply the numerical factor by the conversion factor:

\[0.8 \, \text{g} \times 1000 \, \text{mg/g} = 800 \, \text{mg}\]

This results in the quantity in the new unit, milligrams. The units of grams cancel out during this process, leaving us with the converted units (mg).

• Ensure all operations are done systematically.
• Double-check the multiplication to ensure precision.

Remember, correctly multiplying by the conversion factor is what ultimately provides the accurate conversion.