To convert 13.6 grams per cubic centimeter to kilograms per cubic meter, follow these steps:
1. Understand that 1 kilogram (kg) is equal to 1000 grams (g), and 1 cubic meter (m³) is equal to 10^6 cubic centimeters (cm³).
2. Start with the given density:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \][/tex]
3. Convert grams to kilograms:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \][/tex]
4. Convert cubic centimeters to cubic meters:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} \][/tex]
5. Simplify the expression:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} = \frac{13.6 \times 10^6 \text{ kg}}{1000 \text{ m}^3} \][/tex]
6. Calculate the final value:
[tex]\[ \frac{13.6 \times 10^6}{1000} = 13600 \text{ kg/m}^3 \][/tex]
So the complete filled-in equation is:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} = \frac{13600 \text{ kg}}{\text{m}^3} \][/tex]
The correct labels for the blanks in the equation are:
[tex]\[ \frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} = \frac{13600 \text{ kg}}{\text{m}^3} \][/tex]
