Find 0.078-(5.2*10 to the power of -3) in scientific notation

To solve \(0.078 - (5.2 \times 10^{-3})\) and express the result in scientific notation, we first need to convert \(0.078\) into scientific notation:

\[
0.078 = 7.8 \times 10^{-2}
\]

Next, we can rewrite \(5.2 \times 10^{-3}\) with a common exponent to make subtraction easier. The exponent \(-3\) is smaller than \(-2\), so we can convert \(7.8 \times 10^{-2}\) to an equivalent form with \(10^{-3}\):

\[
7.8 \times 10^{-2} = 7.8 \times 10^{-2} \times \frac{10^{1}}{10^{1}} = 78 \times 10^{-3}
\]

Now we can perform the subtraction:

\[
78 \times 10^{-3} - 5.2 \times 10^{-3} = (78 - 5.2) \times 10^{-3} = 72.8 \times 10^{-3}
\]

Finally, to express \(72.8 \times 10^{-3}\) in proper scientific notation, we rewrite it as:

\[
7.28 \times 10^{-2}
\]

Thus, the final result in scientific notation is:

\[
\boxed{7.28 \times 10^{-2}}
\]