1. The problem is to find the value expressed by the decimal number 4.509. 2. We can represent 4.509 as the sum of its parts: 4 + 0.5 + 0.009. 3. To express these parts as fractions with a common denominator of 1000, write 0.5 as $\frac{500}{1000}$ and 0.009 as $\frac{9}{1000}$. 4. Now sum: $4 + \frac{500}{1000} + \frac{9}{1000} = 4 + \frac{509}{1000}$. 5. Thus, 4.509 equals $4 + \frac{509}{1000}$, which is the simplified fractional form of the decimal 4.509. 6. This confirms that $4.509 = 4 + \frac{509}{1000}$.