To find the total weight of the original cell sample, you can multiply the weight of each batch by the number of batches.
Each batch weighs \(1.8 \times 10^{-8}\) grams, and there are 11 batches.
\[ \text{Total weight} = \text{weight of each batch} \times \text{number of batches} \]
\[ \text{Total weight} = (1.8 \times 10^{-8}) \times 11 \]
Now, calculate \(1.8 \times 11\):
\[ 1.8 \times 11 = 19.8 \]
Next, we can express \(19.8\) in scientific notation.
To convert \(19.8\) to scientific notation, we can express it as \(1.98 \times 10^1\) (since moving the decimal point one place to the left increases the exponent of 10 by 1).
Now combine this with the \(10^{-8}\):
\[ \text{Total weight} = 1.98 \times 10^1 \times 10^{-8} \]
When multiplying exponentials, we add the exponents:
\[ 1.98 \times 10^{1 + (-8)} = 1.98 \times 10^{-7} \]
Thus, the original sample weighed:
\[ \boxed{1.98 \times 10^{-7}} \text{ grams} \]
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