Question

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.

Answer 1

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:

\[
\boxed{2.56 \times 10^{-2}}.
\]