To multiply \( \frac{4}{9} \times 36.63 \), we can first convert 36.63 into a fraction. Since 36.63 is equivalent to \( \frac{3663}{100} \), we can multiply the two fractions directly:
\[ \frac{4}{9} \times \frac{3663}{100} = \frac{4 \times 3663}{9 \times 100} \]
Calculating the numerator: \[ 4 \times 3663 = 14652 \]
Calculating the denominator: \[ 9 \times 100 = 900 \]
Now, we have: \[ \frac{14652}{900} \]
Next, we simplify this fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 36.
Dividing: \[ 14652 \div 36 = 407 \] \[ 900 \div 36 = 25 \]
Thus, we have: \[ \frac{407}{25} \]
Now, we can convert this improper fraction into a decimal by performing the division: \[ 407 \div 25 = 16.28 \]
So, \( \frac{4}{9} \times 36.63 = 16.28 \).
The answer is \( \boxed{16.28} \). Therefore, the correct option is:
OC. 16.28.