`"1 g m"^(-3)=…………."kg cm"^(-3)`

Options

A. `10^9`
B. `10^6`
C. `10^(-6)`
D. `10^(-9)`

Explanation

To convert \(1 \, \text{g/m}^3\) to \(\text{kg/cm}^3\), we can follow these steps:

### Step 1: Understand the conversion factors
We know that:
- \(1 \, \text{kg} = 1000 \, \text{g}\)
- \(1 \, \text{m}^3 = 100 \, \text{cm} \times 100 \, \text{cm} \times 100 \, \text{cm} = 1000000 \, \text{cm}^3 = 10^6 \, \text{cm}^3\)

### Step 2: Convert grams to kilograms
We start with \(1 \, \text{g/m}^3\):
\[ 1 \, \text{g/m}^3 = \frac{1 \, \text{g}}{1 \, \text{m}^3} \]
To convert grams to kilograms, we use the conversion \(1 \, \text{g} = \frac{1}{1000} \, \text{kg}\):
\[ 1 \, \text{g/m}^3 = \frac{1/1000 \, \text{kg}}{1 \, \text{m}^3} = \frac{1}{1000} \, \text{kg/m}^3 \]

### Step 3: Convert cubic meters to cubic centimeters
Next, we convert the denominator from cubic meters to cubic centimeters:
\[ 1 \, \text{m}^3 = 10^6 \, \text{cm}^3 \]
So we can rewrite our expression:
\[ 1 \, \text{g/m}^3 = \frac{1}{1000} \, \text{kg} \cdot \frac{1}{10^6 \, \text{cm}^3} \]

### Step 4: Combine the conversions
Now we can combine the conversions:
\[ 1 \, \text{g/m}^3 = \frac{1}{1000 \times 10^6} \, \text{kg/cm}^3 = \frac{1}{10^9} \, \text{kg/cm}^3 \]

### Step 5: Write the final answer
Thus, we can express \(1 \, \text{g/m}^3\) in terms of \(\text{kg/cm}^3\):
\[ 1 \, \text{g/m}^3 = 10^{-9} \, \text{kg/cm}^3 \]

### Final Answer:
\[ 1 \, \text{g/m}^3 = 10^{-9} \, \text{kg/cm}^3 \]

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