To calculate \( 0.078 - (5.2 \times 10^{-3}) \), we first express \( 0.078 \) in scientific notation.
\[ 0.078 = 7.8 \times 10^{-2} \]
Now, we need to perform the subtraction. To do this easily, we can express both numbers in terms of the same exponent. We will convert \( 7.8 \times 10^{-2} \) to have the same exponent as \( 5.2 \times 10^{-3} \).
To express \( 7.8 \times 10^{-2} \) in terms of \( 10^{-3} \):
\[ 7.8 \times 10^{-2} = 7.8 \times 10^{-2} \times \frac{10^{1}}{10^{1}} = 78 \times 10^{-3} \]
Now we can perform the subtraction:
\[ 78 \times 10^{-3} - 5.2 \times 10^{-3} = (78 - 5.2) \times 10^{-3} = 72.8 \times 10^{-3} \]
Next, we need to express \( 72.8 \times 10^{-3} \) back into proper scientific notation (which requires the coefficient to be between 1 and 10):
\[ 72.8 \times 10^{-3} = 7.28 \times 10^{-2} \]
Thus, the final answer in scientific notation is:
\[ \boxed{7.28 \times 10^{-2}} \]
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