`"1 kg m"^(-3)=…….."g cm"^(-3)`

Options

A. 100
B. 1/100
C. 1000
D. 1/1000

Explanation

To convert \(1 \, \text{kg m}^{-3}\) to \(\text{g cm}^{-3}\), 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:
\[ 1 \, \text{kg} = 1000 \, \text{g} \]

3. **Convert Cubic Meters to Cubic Centimeters**:
We also know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \]
Therefore, to convert cubic meters to cubic centimeters:
\[ 1 \, \text{m}^3 = (100 \, \text{cm})^3 = 100^3 \, \text{cm}^3 = 1000000 \, \text{cm}^3 = 10^6 \, \text{cm}^3 \]

4. **Set Up the Conversion**:
Now we can set up the conversion for \(1 \, \text{kg m}^{-3}\):
\[ 1 \, \text{kg m}^{-3} = \frac{1 \, \text{kg}}{1 \, \text{m}^3} = \frac{1000 \, \text{g}}{10^6 \, \text{cm}^3} \]

5. **Simplify the Expression**:
Now, simplify the fraction:
\[ \frac{1000 \, \text{g}}{10^6 \, \text{cm}^3} = \frac{1000}{1000000} \, \text{g cm}^{-3} = \frac{1}{1000} \, \text{g cm}^{-3} = 0.001 \, \text{g cm}^{-3} \]

6. **Final Answer**:
Therefore, we conclude that:
\[ 1 \, \text{kg m}^{-3} = 0.001 \, \text{g cm}^{-3} \]

### Final Result:
\[ 1 \, \text{kg m}^{-3} = 0.001 \, \text{g cm}^{-3} \]