Problem 28 - Prealgebra

Question

Use the conversion factors in Tables 1 and 2 to make the following conversions. (TABLE CANT COPY) \(1,979\) mg to grams

Step-by-Step Solution

Answer

1,979 mg is equal to 1.979 grams.

Step 1: Identify the Conversion Factor

To convert milligrams (mg) to grams (g), use the conversion factor: 1 gram = 1000 milligrams. This is the key information needed to perform the conversion.

Step 2: Set Up the Conversion Equation

Write the conversion equation using the identified conversion factor. Since 1 g = 1000 mg, we use the conversion factor as a fraction:\[\text{Conversion equation: } \frac{1 \, \text{gram}}{1000 \, \text{milligrams}}\]

Step 3: Perform the Calculation

Multiply the given amount in milligrams by the conversion factor to convert it to grams:\[1979 \, \text{mg} \times \frac{1 \, \text{g}}{1000 \, \text{mg}} = 1.979 \, \text{g}\]This step involves multiplying 1979 by \(\frac{1}{1000}\) to find the equivalent amount in grams.

Key Concepts

Milligrams to Grams Conversion

When needing to convert measurements from milligrams to grams, it's important to understand the basic relationship between these two units. The milligram (mg) and gram (g) are both metric units of mass. The main difference is their magnitude. One gram is a larger unit compared to a milligram. In fact, one gram equals 1000 milligrams. To convert milligrams to grams:

• Recognize that 1 gram (g) is equivalent to 1000 milligrams (mg).
• This means you can simply divide the number of milligrams by 1000 to find grams.

Let's say you want to convert 1979 mg to grams. Since 1 gram is 1000 milligrams, you divide 1979 mg by 1000:\[1979 \, \text{mg} \times \left( \frac{1 \, \text{g}}{1000 \, \text{mg}} \right) = 1.979 \, \text{g}\] This calculation shows that 1979 milligrams is equivalent to 1.979 grams.

Conversion Factor

Conversion factors play a critical role in transforming measurements from one unit to another. Understanding this concept is essential, as it allows you to navigate unit conversions effortlessly. A conversion factor is a fraction or a factor that expresses how many of one unit is equal to another unit. They are often based on standard values agreed upon universally.For example, the conversion factor from milligrams to grams is:\[\frac{1 \, \text{gram}}{1000 \, \text{milligrams}}\]This fraction is read as "1 gram per 1000 milligrams," meaning it's the amount that 1 gram represents in milligrams. When using a conversion factor:

• Multiply the measurement you need to convert by the conversion factor.
• Ensure the units you want to cancel are in the opposite position in the fraction.

In our example, multiplying 1979 mg by the factor \(\frac{1 \text{ gram}}{1000 \text{ mg}}\) cancels the milligrams and leaves the result in grams.

Prealgebra Problems

Prealgebra lays the groundwork for more complex math concepts by introducing basic arithmetic and number operations. It's the stage where students start to work with integers, fractions, and begin to understand the idea of variables. Unit conversion exercises, such as converting milligrams to grams, serve as great prealgebra problems. They require:

• Simple multiplication or division.
• Understanding and applying conversion factors correctly.
• Keeping track of units throughout the calculation.

For instance, converting 1979 milligrams into grams requires dividing by the conversion factor 1000, which not only employs division skills but also reinforces the understanding of scale and size in measurements. Prealgebra problems encourage students to practice these skills repeatedly, paving the way for more complex problem-solving techniques.