To find the half-life of uranium-238, we start with the half-life of uranium-235, which is given as 700,000,000 years.
The half-life of uranium-238 is given to be 4.463 times \(10^{11}\) years longer than that of uranium-235. We can calculate it as follows:
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Calculate \(4.463 \times 10^{11}\) years in decimal form: \[ 4.463 \times 10^{11} = 446,300,000,000 \text{ years} \]
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Now, we add this value to the half-life of uranium-235: \[ \text{Half-life of uranium-238} = 700,000,000 + 446,300,000,000 \]
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Perform the addition: \[ 700,000,000 + 446,300,000,000 = 447,000,000,000 \text{ years} \]
Thus, the half-life of uranium-238 in decimal form is:
\[ \boxed{447000000000} \] years or \(4.47 \times 10^{11}\) years if expressed in scientific notation.
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