To subtract the numbers \(8.03 \times 10^{-8}\) and \(2.56 \times 10^{-2}\), we first need to express them with the same exponent.
The number \(2.56 \times 10^{-2}\) can be written with an exponent of \(-8\) by multiplying it by \(10^{6}\):
\[ 2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^6}{10^6} = 2.56 \times 10^4 \times 10^{-8} = 256000 \times 10^{-8} \]
Now we can perform the subtraction:
\[ 8.03 \times 10^{-8} - 256000 \times 10^{-8} = (8.03 - 256000) \times 10^{-8} \]
Calculating \(8.03 - 256000\):
\[ 8.03 - 256000 = -255991.97 \]
So, the result is:
\[ -255991.97 \times 10^{-8} \]
To simplify this result, we convert it back to scientific notation:
\[ -2.5599197 \times 10^{-3} \]
Thus, the final answer is:
\[ \boxed{-2.56 \times 10^{-3}} , (\text{rounded to 3 significant figures}) \]
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