To subtract $8.03 \times 10^{-8}$ from $2.56 \times 10^{-2}$, we need both numbers to have the same power of 10. The second number, $2.56 \times 10^{-2}$, is much bigger because of the higher power of 10. When we try to match the powers, $2.56 \times 10^{-2}$ is still so much larger that $8.03 \times 10^{-8}$ is almost too small to make a difference. So, the final answer will be close to $2.56 \times 10^{-2}$, because the first number is so tiny in comparison.

Question

GPT-4o mini · Answer

To effectively subtract $8.03 \times 10^{-8}$ from $2.56 \times 10^{-2}$, we first align the powers of 10. Since $2.56 \times 10^{-2}$ has a power of $-2$ and $8.03 \times 10^{-8}$ has a power of $-8$, we can convert $8.03 \times 10^{-8}$ to the same power as $2.56 \times 10^{-2}$. We can rewrite $8.03 \times 10^{-8}$ in terms of $10^{-2}$ by multiplying it by $10^{-6}$: $$ 8.03 \times 10^{-8} = 8.03 \times 10^{-8 + 6} \times 10^{-6} = 8.03 \times 10^{-2} \times 10^{-6} = 0.0000803. $$ Now we can express $2.56 \times 10^{-2}$ as a decimal as well: $$ 2.56 \times 10^{-2} = 0.0256. $$ Now we can perform the subtraction: $$ 0.0256 - 0.0000000803. $$ Since $0.0000000803$ is extremely small in comparison to $0.0256$, we can say: $$ 0.0256 - 0.0000000803 \approx 0.0256. $$ To get a precise result in scientific notation, we can express it as: $$ \approx 2.56 \times 10^{-2}. $$ Therefore, the final answer, accounting for the negligible effect of $8.03 \times 10^{-8}$, is: $$ \boxed{2.56 \times 10^{-2}}. $$