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