To find the half-life of uranium-238, we need to add the half-life of uranium-235 to the additional time given for uranium-238.
The half-life of uranium-235 is given as: \[ 700,000,000 \text{ years} \]
The additional half-life for uranium-238 is: \[ 4.463 \times 10^{11} \text{ years} \] This can also be expressed in decimal form: \[ 4.463 \times 10^{11} = 446,300,000,000 \text{ years} \]
Now, we add the two half-lives together: \[ \text{Half-life of U-238} = \text{Half-life of U-235} + \text{Additional time} \] \[ = 700,000,000 + 446,300,000,000 \] \[ = 447,000,000,000 \text{ years} \]
Thus, the half-life of uranium-238 is: \[ \boxed{447,000,000,000} \]