Density of a liquid in CGS system is `0.625(g)/(cm^3)`. What is its magnitude is SI system?

Options

A. 0.625
B. 0.0625
C. 0.00625
D. 625

Explanation

To convert the density of a liquid from the CGS system to the SI system, we need to follow these steps:

### Step 1: Understand the given density in CGS
The density of the liquid is given as:
\[ \rho = 0.625 \, \frac{\text{g}}{\text{cm}^3} \]

### Step 2: Convert grams to kilograms
In the SI system, mass is measured in kilograms. We know that:
\[ 1 \, \text{g} = 0.001 \, \text{kg} \]
Therefore, we convert grams to kilograms:
\[ 0.625 \, \text{g} = 0.625 \times 0.001 \, \text{kg} = 0.000625 \, \text{kg} \]

### Step 3: Convert cubic centimeters to cubic meters
In the SI system, volume is measured in cubic meters. We know that:
\[ 1 \, \text{cm} = 0.01 \, \text{m} \]
Thus,
\[ 1 \, \text{cm}^3 = (0.01 \, \text{m})^3 = 0.000001 \, \text{m}^3 = 10^{-6} \, \text{m}^3 \]

### Step 4: Substitute the values into the density formula
Now we can substitute the converted values into the density formula:
\[ \rho = \frac{0.000625 \, \text{kg}}{10^{-6} \, \text{m}^3} \]

### Step 5: Calculate the density in SI units
Now, we perform the division:
\[ \rho = 0.000625 \, \text{kg} \times 10^{6} \, \text{m}^{-3} = 625 \, \text{kg/m}^3 \]

### Conclusion
The magnitude of the density in the SI system is:
\[ \boxed{625 \, \text{kg/m}^3} \]