To find \(0.078 - (5.2 \times 10^{-3})\), we first convert \(0.078\) to scientific notation.
\(0.078\) can be expressed as: \[ 0.078 = 7.8 \times 10^{-2} \]
Now we have: \[ 7.8 \times 10^{-2} - 5.2 \times 10^{-3} \]
Next, we need to express both terms with the same exponent. The term \(5.2 \times 10^{-3}\) can be converted to the same exponent as \(7.8 \times 10^{-2}\):
To do this, we can convert \(5.2 \times 10^{-3}\) to an equivalent expression with \(10^{-2}\): \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \]
Now we can subtract: \[ (7.8 \times 10^{-2}) - (0.052 \times 10^{-2}) = (7.8 - 0.052) \times 10^{-2} \]
Calculating \(7.8 - 0.052\): \[ 7.8 - 0.052 = 7.748 \]
Now we can write our result: \[ 7.748 \times 10^{-2} \]
In scientific notation, this is best expressed as: \[ 7.748 \times 10^{-2} \]
Thus, the final answer is: \[ \boxed{7.748 \times 10^{-2}} \]
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