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Complete the steps for converting 13.6 g/cm³ to kg/m³. (1 kg = 1,000 g, 1 m³ = 10⁶ cm³)

Labels:
- 13,600
- 10⁶
- 1,360
- 1 g
- 1 kg
- 1 m³

Equation:
[tex]\[
\frac{13.6 \text{ g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1,000 \text{ g}} \times \frac{10^6 \text{ cm}^3}{1 \text{ m}^3} = \frac{13,600 \text{ kg}}{\text{m}^3}
\][/tex]



Answer :

GinnyAnswer
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]

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