A student sets up the following equation to convert a measurement.
(The? stands for a number the student is going to calculate.)
Fill in the missing part of this equation.

Ask by Todd Parsons. in the United States

Jan 20,2025

Question

A student sets up the following equation to convert a measurement.
(The? stands for a number the student is going to calculate.)
Fill in the missing part of this equation.

Ask by Todd Parsons. in the United States

Jan 20,2025

UpStudy AI · Accepted Answer

To convert the measurement from $$\frac{\mathrm{g}}{\mathrm{cm}^3}$$ to $$\frac{\mathrm{B}}{\mathrm{m}^3}$$, you'll need to use appropriate conversion factors for both mass and volume units. Here's how you can fill in the missing part of the equation:

$$
\left(-5.6 \times 10^{3} \frac{\mathrm{g}}{\mathrm{cm}^{3}}\right) \cdot \left( \frac{1 \times 10^{-3} \, \mathrm{kg}}{1 \, \mathrm{g}} \times \frac{1 \, \mathrm{m}^3}{1 \times 10^{-6} \, \mathrm{cm}^3} \right) = ? \frac{\mathrm{B}}{\mathrm{m}^{3}}
$$

### Step-by-Step Conversion:

1. **Convert Grams to Kilograms:**
   $$
   1 \, \mathrm{kg} = 10^3 \, \mathrm{g} \quad \Rightarrow \quad \frac{1 \, \mathrm{kg}}{10^3 \, \mathrm{g}} = 1 \times 10^{-3} \, \frac{\mathrm{kg}}{\mathrm{g}}
   $$
   
2. **Convert Cubic Centimeters to Cubic Meters:**
   $$
   1 \, \mathrm{m}^3 = 10^6 \, \mathrm{cm}^3 \quad \Rightarrow \quad \frac{1 \, \mathrm{m}^3}{10^6 \, \mathrm{cm}^3} = 1 \times 10^{-6} \, \frac{\mathrm{m}^3}{\mathrm{cm}^3}
   $$
   
3. **Combine the Conversion Factors:**
   $$
   \frac{1 \times 10^{-3} \, \mathrm{kg}}{\mathrm{g}} \times \frac{1 \, \mathrm{m}^3}{1 \times 10^{-6} \, \mathrm{cm}^3} = 1 \times 10^{3} \, \frac{\mathrm{kg}}{\mathrm{m}^3 \cdot \frac{\mathrm{g}}{\mathrm{cm}^3}}
   $$

### Final Equation:

$$
\left(-5.6 \times 10^{3} \frac{\mathrm{g}}{\mathrm{cm}^{3}}\right) \cdot \left( \frac{1 \times 10^{-3} \, \mathrm{kg}}{1 \, \mathrm{g}} \times \frac{1 \, \mathrm{m}^3}{1 \times 10^{-6} \, \mathrm{cm}^3} \right) = ? \frac{\mathrm{B}}{\mathrm{m}^{3}}
$$

### Simplified Conversion:

After applying the conversion factors:
$$
-5.6 \times 10^{3} \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} \times 1 \times 10^{3} \, \frac{\mathrm{kg}}{\mathrm{m}^{3}} = -5.6 \times 10^{6} \, \frac{\mathrm{kg}}{\mathrm{m}^{3}}
$$

**Note:** Replace $$\mathrm{B}$$ with the appropriate unit if it was meant to represent a specific unit like kilograms ($$\mathrm{kg}$$).
$$ \left(-5.6 \times 10^{3} \frac{\mathrm{g}}{\mathrm{cm}^{3}}\right) \cdot \left( \frac{1 \times 10^{-3} \, \mathrm{kg}}{1 \, \mathrm{g}} \times \frac{1 \, \mathrm{m}^3}{1 \times 10^{-6} \, \mathrm{cm}^3} \right) = -5.6 \times 10^{6} \frac{\mathrm{kg}}{\mathrm{m}^{3}} $$

A student sets up the following equation to convert a measurement.
(The? stands for a number the student is going to calculate.)
Fill in the missing part of this equation.

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A student sets up the following equation to convert a measurement. (The? stands for a number the student is going to calculate.) Fill in the missing part of this equation.

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A student sets up the following equation to convert a measurement.
(The? stands for a number the student is going to calculate.)
Fill in the missing part of this equation.