Vanadium metal is added to steel to impart strength. The density of vanadium is `5.96g//cm^(3)`. Express this in S.I units `(kg//m^(3))`.

Explanation

To convert the density of vanadium from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we can follow these steps:

### Step 1: Write down the given density
The density of vanadium is given as:
\[ \rho = 5.96 \, \text{g/cm}^3 \]

### Step 2: Convert grams to kilograms
We know that:
\[ 1 \, \text{kg} = 1000 \, \text{g} \]
So, to convert grams to kilograms, we divide by 1000:
\[ 5.96 \, \text{g/cm}^3 = \frac{5.96}{1000} \, \text{kg/cm}^3 \]

### Step 3: Convert cubic centimeters to cubic meters
We also know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \]
Thus,
\[ 1 \, \text{cm}^3 = (0.01 \, \text{m})^3 = 0.000001 \, \text{m}^3 = 10^{-6} \, \text{m}^3 \]
So, we can convert cm³ to m³:
\[ 1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3 \]

### Step 4: Combine the conversions
Now we can substitute these conversions into our density equation:
\[ \rho = \frac{5.96}{1000} \, \text{kg/cm}^3 = \frac{5.96}{1000} \, \text{kg} \times \frac{1}{10^{-6} \, \text{m}^3} \]

### Step 5: Simplify the expression
This simplifies to:
\[ \rho = 5.96 \times 10^{3} \, \text{kg/m}^3 \]

### Final Answer
Thus, the density of vanadium in SI units is:
\[ \rho = 5960 \, \text{kg/m}^3 \]

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