Metric SI Unit Conversions - Free Printable

The image you provided is an answer key for a worksheet on unit conversion problems. The task involves solving unit conversion problems using cross-multiplication. Below, I will explain the solution process for one of the problems as an example and then generalize the approach.

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Example Problem:

Convert 1.5 grams to milligrams.

#### Step-by-Step Solution:

1. Understand the Conversion Factor:
- 1 gram (g) = 1000 milligrams (mg).

2. Set Up the Proportion:
- We know that \( 1 \text{ g} = 1000 \text{ mg} \).
- We need to find how many milligrams are in 1.5 grams.
- Set up the proportion:
\[
\frac{1 \text{ g}}{1000 \text{ mg}} = \frac{1.5 \text{ g}}{x \text{ mg}}
\]
where \( x \) is the number of milligrams we are solving for.

3. Cross-Multiply:
- Cross-multiplying gives:
\[
1 \cdot x = 1.5 \cdot 1000
\]
\[
x = 1500
\]

4. Conclusion:
- Therefore, \( 1.5 \text{ g} = 1500 \text{ mg} \).

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General Approach for Unit Conversion Using Cross-Multiplication:

1. Identify the Conversion Factor:
- Know the relationship between the two units (e.g., 1 g = 1000 mg, 1 kg = 1000 g, etc.).

2. Set Up the Proportion:
- Write the known conversion factor as a ratio.
- Write the unknown value as a variable in a second ratio.
- Ensure the units match across the numerator and denominator.

3. Cross-Multiply:
- Multiply the numerator of the first fraction by the denominator of the second fraction.
- Multiply the denominator of the first fraction by the numerator of the second fraction.
- Solve for the unknown variable.

4. Solve for the Unknown:
- Simplify the equation to find the value of the unknown.

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Additional Examples from the Image:

#### Example 1: Convert 0.75 grams to milligrams.
- Conversion factor: \( 1 \text{ g} = 1000 \text{ mg} \).
- Proportion: \( \frac{1 \text{ g}}{1000 \text{ mg}} = \frac{0.75 \text{ g}}{x \text{ mg}} \).
- Cross-multiply: \( 1 \cdot x = 0.75 \cdot 1000 \).
- Solve: \( x = 750 \).
- Answer: \( 0.75 \text{ g} = 750 \text{ mg} \).

#### Example 2: Convert 1.25 grams to milligrams.
- Conversion factor: \( 1 \text{ g} = 1000 \text{ mg} \).
- Proportion: \( \frac{1 \text{ g}}{1000 \text{ mg}} = \frac{1.25 \text{ g}}{x \text{ mg}} \).
- Cross-multiply: \( 1 \cdot x = 1.25 \cdot 1000 \).
- Solve: \( x = 1250 \).
- Answer: \( 1.25 \text{ g} = 1250 \text{ mg} \).

#### Example 3: Convert 0.65 grams to milligrams.
- Conversion factor: \( 1 \text{ g} = 1000 \text{ mg} \).
- Proportion: \( \frac{1 \text{ g}}{1000 \text{ mg}} = \frac{0.65 \text{ g}}{x \text{ mg}} \).
- Cross-multiply: \( 1 \cdot x = 0.65 \cdot 1000 \).
- Solve: \( x = 650 \).
- Answer: \( 0.65 \text{ g} = 650 \text{ mg} \).

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Final Answer:

The solutions to the problems are already provided in the image, and the method used is consistent with the steps outlined above. If you have any specific questions about a particular problem, feel free to ask!

\boxed{\text{See explanations above for detailed solutions.}}