To solve the expression \(0.078 - (5.2 \times 10^{-3})\), we first need to express \(0.078\) in scientific notation.
We can write \(0.078\) as: \[ 0.078 = 7.8 \times 10^{-2} \]
Now, we will align the exponents to perform the subtraction. The term \((5.2 \times 10^{-3})\) can be kept as is.
Since \(10^{-2}\) and \(10^{-3}\) have different exponents, we can express \(7.8 \times 10^{-2}\) in terms of \(10^{-3}\): \[ 7.8 \times 10^{-2} = 7.8 \times 10^{-2} \cdot \frac{10^{-1}}{10^{-1}} = 78 \times 10^{-3} \]
So now, we rewrite the original expression with a common exponent: \[ 0.078 - (5.2 \times 10^{-3}) = (78 \times 10^{-3}) - (5.2 \times 10^{-3}) \] Next, we can subtract the coefficients: \[ 78 - 5.2 = 72.8 \]
Thus, we have: \[ 72.8 \times 10^{-3} \]
Now, we express \(72.8\) in scientific notation: \[ 72.8 = 7.28 \times 10^{1} \]
Combining this with \(10^{-3}\): \[ 72.8 \times 10^{-3} = 7.28 \times 10^{1} \times 10^{-3} = 7.28 \times 10^{-2} \]
Therefore, the final answer in scientific notation is: \[ \boxed{7.28 \times 10^{-2}} \]