1kg `m^(-3)=………..`

Options

A. 1000 g `m^(-3)`
B. `1/(1000)" g m"^(-3)`
C. `1000" kg m"^(-3)`
D. `1" g m"^(-3)`

Answer

To convert 1 kg/m³ into grams/cm³, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the units**: We need to convert kilograms (kg) to grams (g) and cubic meters (m³) to cubic centimeters (cm³).

2. **Convert kilograms to grams**:
- We know that 1 kg = 1000 grams.
- Therefore, 1 kg/m³ = 1000 g/m³.

3. **Convert cubic meters to cubic centimeters**:
- We know that 1 meter = 100 centimeters.
- Therefore, 1 m³ = (100 cm)³ = 1000000 cm³ = 10^6 cm³.

4. **Combine the conversions**:
- Now we can substitute these conversions into our original expression:
- 1 kg/m³ = 1000 g / (10^6 cm³).

5. **Simplify the expression**:
- This simplifies to:
- 1 kg/m³ = 1000 g / 10^6 cm³ = 1 g / 1000 cm³.

6. **Final result**:
- Therefore, we can express this as:
- 1 kg/m³ = 1/1000 g/cm³.

### Final Answer:
1 kg/m³ = 1/1000 g/cm³.

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