To find the original weight of the cell sample, we need to multiply the weight of one batch by the number of batches.
Each batch weighs \(9.3 \times 10^{-5}\) grams, and there are 9 batches:
\[ \text{Original weight} = \text{Weight of one batch} \times \text{Number of batches} \]
\[ \text{Original weight} = (9.3 \times 10^{-5} , \text{grams}) \times 9 \]
Now, we can calculate this:
- First, multiply the numerical parts:
\[ 9.3 \times 9 = 83.7 \]
- Since \(9 = 9.0 \times 10^0\), we maintain the \(10^{-5}\):
\[ \text{Original weight} = 83.7 \times 10^{-5} , \text{grams} \]
- We now need to express \(83.7\) in scientific notation. \(83.7\) can be written as \(8.37 \times 10^1\):
\[ \text{Original weight} = (8.37 \times 10^1) \times 10^{-5} \]
- When multiplying the powers of ten, we add the exponents:
\[ 10^1 \times 10^{-5} = 10^{1-5} = 10^{-4} \]
- Now, combine these together:
\[ \text{Original weight} = 8.37 \times 10^{-4} , \text{grams} \]
Thus, the original sample weighed
\[ \boxed{8.37 \times 10^{-4}} \text{ grams}. \]
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