To find the half-life of uranium-238, we need to add the half-life of uranium-235 to the additional time given.
The half-life of uranium-235 is:
\[ 700,000,000 \text{ years} \]
The additional time for uranium-238 is:
\[ 4.463 \times 10^{11} \text{ years} = 446,300,000,000 \text{ years} \]
Now, we add these two half-lives together:
\[ \text{Half-life of uranium-238} = 700,000,000 + 446,300,000,000 \]
Converting \(700,000,000\) to the same format as \(446,300,000,000\):
\[ 700,000,000 = 0.7 \times 10^9 = 0.7 \times 10^9 = 0.0007 \times 10^{12} \]
Adding the two half-lives in the same exponent format:
\[ \text{Half-life of uranium-238} = 0.0007 \times 10^{12} + 446.3 \times 10^{9} \]
Calculating the first part represented on the same power of 10:
\[ 0.7 \times 10^9 = 0.0007 \times 10^{12} \]
Thus, when converting it to represent both with the exponent \(10^{12}\):
\[ 446301.0 \times 10^{9} \text{ (where the first term has been adjusted)} \]
Adding these values:
\[ 4.463 \times 10^{11} + 0.7 \times 10^{9} = 4.4637 \times 10^{11} \text{ (keeping precision)} \]
So the half-life of uranium-238 is:
\[ \text{Half-life of uranium-238} = 4.468 \times 10^{11} \]
In decimal form, this can be represented as:
\[ 446300000000.0 \text{ years} \]
Thus the half-life of uranium-238 is:
\[ \boxed{4.4683 \times 10^{11}} \]
or simply:
\[ 446300000000 \text{ years} \]
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