To find the weight of the original sample, you need to multiply the weight of one batch by the number of batches. The weight of one batch is \(3.9 \times 10^{-10}\) grams, and there are 8 batches.
So, the calculation is:
\[ \text{Total weight} = \text{Weight of one batch} \times \text{Number of batches} \]
\[ \text{Total weight} = (3.9 \times 10^{-10}) \times 8 \]
Now, multiply the numbers:
\[ 3.9 \times 8 = 31.2 \]
Now we express \(31.2\) in scientific notation:
\[ 31.2 = 3.12 \times 10^1 \]
Now, combining this with the \(10^{-10}\) from the original weight:
\[ \text{Total weight} = 3.12 \times 10^1 \times 10^{-10} \]
When multiplying exponents, you add the powers:
\[ 3.12 \times 10^{1 - 10} = 3.12 \times 10^{-9} \]
Thus, the weight of the original sample is:
\[ \boxed{3.12 \times 10^{-9}} \text{ grams} \]