Convert 2 x 10^7 mg/cm³ to kg/m³.
Understand the Problem
The question requires converting a density value from milligrams per cubic centimeter (mg/cm³) to kilograms per cubic meter (kg/m³). This involves understanding the relationships between milligrams and kilograms, and between cubic centimeters and cubic meters. The conversion requires multiplying by a factor to adjust for the differences in units.
Answer
$2 \times 10^7 \text{ kg/m}^3$
Answer for screen readers
$2 \times 10^7 \text{ kg/m}^3$
Steps to Solve
- Convert mg to kg
To convert milligrams (mg) to kilograms (kg), we divide by $10^6$ since 1 kg = $10^6$ mg.
$2 \times 10^7 \text{ mg/cm}^3 = \frac{2 \times 10^7}{10^6} \text{ kg/cm}^3 = 2 \times 10^1 \text{ kg/cm}^3 = 20 \text{ kg/cm}^3$
- Convert cm³ to m³
To convert cubic centimeters (cm³) to cubic meters (m³), we need to remember that 1 m = 100 cm. Therefore, 1 m³ = $(100 \text{ cm})^3 = 10^6 \text{ cm}^3$. So, to convert from cm³ to m³, we multiply by $10^6$.
$20 \frac{\text{kg}}{\text{cm}^3} = 20 \frac{\text{kg}}{\text{cm}^3} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} = 20 \times 10^6 \frac{\text{kg}}{\text{m}^3} = 2 \times 10^7 \frac{\text{kg}}{\text{m}^3}$
$2 \times 10^7 \text{ kg/m}^3$
More Information
The conversion factor from mg/cm³ to kg/m³ is $10^6$. This is because 1 cm³ is $10^{-6}$ m³ and 1 mg is $10^{-6}$ kg.
Tips
A common mistake is to confuse the conversion factors between mg and kg or between cm³ and m³. Also one could forget to cube the conversion from cm to m when dealing with volumes: 1 m = 100 cm, so 1 m³ = (100 cm)³ = 1,000,000 cm³ = $10^6$ cm³.
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