To subtract the two numbers \(8.03 \times 10^{-8}\) and \(2.56 \times 10^{-2}\), we first need to express them with the same exponent.
The first number \(8.03 \times 10^{-8}\) is already in scientific notation with an exponent of \(-8\). We can rewrite the second number \(2.56 \times 10^{-2}\) with the same exponent:
\[ 2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^{-6}}{10^{-6}} = 2.56 \times 10^{-8} \times 10^{4} = 2.56 \times 10^{-8} \times 10000 \]
Now combining the two:
\[ 2.56 \times 10^{-2} = 256000 \times 10^{-8} \]
Now, we can rewrite the original subtraction:
\[ 8.03 \times 10^{-8} - 256000 \times 10^{-8} = (8.03 - 256000) \times 10^{-8} \] \[ = -255991.97 \times 10^{-8} \]
This can be converted back to standard scientific notation:
\[ = -2.5599197 \times 10^{-3} \]
So the result of the subtraction is:
\[ \approx -2.56 \times 10^{-3} \]
if we round it to three significant figures.