To calculate \(5.3 \times 10^{-3} - 6.7 \times 10^{-6}\), we should first express both numbers in the same power of ten.
We can convert \(5.3 \times 10^{-3}\) to the same power of ten as \(6.7 \times 10^{-6}\):
\[ 5.3 \times 10^{-3} = 5.3 \times 10^{-3} \times \frac{1000}{1000} = 5.3 \times 10^{-3} \times 10^{3} \times 10^{-3} = 5.3 \times 10^{0} \text{ (shifting the decimal 3 places to the right)} = 5300 \times 10^{-6} \]
Now we can rewrite the expression:
\[ 5300 \times 10^{-6} - 6.7 \times 10^{-6} = (5300 - 6.7) \times 10^{-6} = 5293.3 \times 10^{-6} \]
Next, we convert \(5293.3\) into scientific notation:
\[ 5293.3 = 5.2933 \times 10^{3} \]
Thus, we have:
\[ 5293.3 \times 10^{-6} = 5.2933 \times 10^{3} \times 10^{-6} = 5.2933 \times 10^{-3} \]
Now rounding \(5.2933\) to two decimal places gives:
\[ 5.29 \times 10^{-3} \]
So the final answer is:
\[ \boxed{5.29 \times 10^{-3}} \]
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