Question

Subtract 3.2 x 10^4 - 2.56 x 10^-2 in scientific notation

Answer 1

To perform the subtraction \(3.2 \times 10^4 - 2.56 \times 10^{-2}\) in scientific notation, we first need to express both numbers with the same exponent.

The number in \(10^{-2}\) can be converted to \(10^4\) by adjusting its coefficient:

\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^4}{10^4} = 2.56 \times 10^{4-6} = 2.56 \times 10^{4} \times 10^{-6} = 0.0000256 \times 10^4
\]

Now we rewrite our subtraction:

\[
3.2 \times 10^4 - 0.0000256 \times 10^4
\]

Now we can combine the two numbers since they are now using the same exponent:

\[
3.2 \times 10^4 - 0.0000256 \times 10^4 = (3.2 - 0.0000256) \times 10^4
\]

To simplify:

\[
3.2 - 0.0000256 = 3.1999744
\]

Now we express it in scientific notation:

\[
3.1999744 \times 10^4
\]

Rounding the coefficient to three significant figures, we get:

\[
3.20 \times 10^4
\]

Thus, the final answer is:

\[
\boxed{3.20 \times 10^4}
\]