To find the half-life of uranium-238, we need to add the extra 4.463×10^11 years to the half-life of uranium-235.
The half-life of uranium-235 is given as 700,000,000 years.
To add the extra 4.463×10^11 years, we can use scientific notation addition:
(700,000,000) + (4.463×10^11)
To add numbers in scientific notation, we need to make sure the exponents are the same. Here, we can convert 700,000,000 to scientific notation by moving the decimal point after the 7, which gives us:
7.00×10^8
Now, we can add the numbers:
(7.00×10^8) + (4.463×10^11)
To add them, we need to adjust the exponents to make them the same. In this case, we can convert 7.00×10^8 to 70.0×10^6 by moving the decimal point two places to the left:
(70.0×10^6) + (4.463×10^11)
Now, both exponents are 11, so we can add the coefficients:
70.0 + 4.463 = 74.463
Finally, we write the result in scientific notation:
7.4463×10^1
So, the half-life of uranium-238 is approximately 7.4463 years in decimal form.