Complete the following sentences:
Density in `kgm^(-3)`= ………`xx` density in `gcm^(-3)`

Answer

To complete the sentence "Density in `kgm^(-3)` = ……… `xx` density in `gcm^(-3)`", we need to establish the relationship between the two units of density: kilograms per cubic meter (kg/m³) and grams per cubic centimeter (g/cm³).

### Step-by-Step Solution:

1. **Understand the conversion between kilograms and grams**:
- 1 kilogram (kg) is equal to 1000 grams (g).
- Therefore, we can express 1 kg as 1000 g.

2. **Understand the conversion between meters and centimeters**:
- 1 meter (m) is equal to 100 centimeters (cm).
- Therefore, we can express 1 m as 100 cm.

3. **Convert kg/m³ to g/cm³**:
- We start with the density in kg/m³:
\[ 1 \, \text{kg/m}^3 = \frac{1 \, \text{kg}}{(1 \, \text{m})^3} \]
- Substituting the conversions:
\[ 1 \, \text{kg/m}^3 = \frac{1000 \, \text{g}}{(100 \, \text{cm})^3} \]
- Now calculate \((100 \, \text{cm})^3\):
\[ (100 \, \text{cm})^3 = 100^3 \, \text{cm}^3 = 1000000 \, \text{cm}^3 \]
- Therefore, we can rewrite the density:
\[ 1 \, \text{kg/m}^3 = \frac{1000 \, \text{g}}{1000000 \, \text{cm}^3} = \frac{1000}{1000000} \, \text{g/cm}^3 = \frac{1}{1000} \, \text{g/cm}^3 \]

4. **Final relationship**:
- This means that:
\[ 1 \, \text{kg/m}^3 = \frac{1}{1000} \, \text{g/cm}^3 \]
- To express it in the form of the original question, we multiply both sides by 1000:
\[ 1 \, \text{kg/m}^3 = 1000 \times \text{density in g/cm}^3 \]

5. **Conclusion**:
- Therefore, we can complete the sentence as follows:
\[ \text{Density in } \text{kg/m}^3 = 1000 \times \text{density in } \text{g/cm}^3 \]

### Final Answer:
Density in `kgm^(-3)` = 1000 × density in `gcm^(-3)`