The density of a substance in C.G.S. system is 0.475 `gram//cm^(3)`. What is its value in SI system?

Options

A. `0.475 kg//m^(3)`
B. `475 kg//m^(3)`
C. `0.0475 kg//m^(3)`
D. `4.75 kg//m^(3)`

Explanation

To convert the density from the C.G.S. system to the SI system, we need to follow these steps:

### Step 1: Understand the given density in C.G.S. system
The density given is 0.475 grams per cubic centimeter (g/cm³).

### Step 2: Convert grams to kilograms
In the SI system, the unit of mass is kilograms (kg). We know that:
1 gram = 0.001 kilograms

Thus, to convert grams to kilograms:
\[ 0.475 \, \text{g} = 0.475 \times 0.001 \, \text{kg} = 0.000475 \, \text{kg} \]

### Step 3: Convert cubic centimeters to cubic meters
In the SI system, the unit of volume is cubic meters (m³). We know that:
1 cm = 0.01 m, therefore:
1 cm³ = (0.01 m)³ = 0.000001 m³ = 10^{-6} m³

Thus, to convert cubic centimeters to cubic meters:
\[ 1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3 \]

### Step 4: Calculate the density in SI units
Now, we can convert the density from g/cm³ to kg/m³ using the conversions we have made:
\[ \text{Density in SI} = \frac{\text{mass in kg}}{\text{volume in m}^3} = \frac{0.475 \times 0.001 \, \text{kg}}{10^{-6} \, \text{m}^3} \]
\[ = \frac{0.000475 \, \text{kg}}{10^{-6} \, \text{m}^3} = 0.000475 \times 10^{6} \, \text{kg/m}^3 = 475 \, \text{kg/m}^3 \]

### Final Answer
The density of the substance in the SI system is **475 kg/m³**.

---