To find the original weight of the cell sample, we can multiply the weight of each batch by the number of batches.
Given:
- Weight of each batch = \( 9.3 \times 10^{-5} \) grams
- Number of batches = 99
Now, we calculate the total weight:
\[ \text{Total weight} = \text{Weight of each batch} \times \text{Number of batches} = 9.3 \times 10^{-5} , \text{grams} \times 99 \]
First, we can multiply \( 9.3 \) by \( 99 \):
\[ 9.3 \times 99 = 920.7 \]
Next, we keep the exponent part the same:
\[ \text{Total weight} = 920.7 \times 10^{-5} , \text{grams} \]
Now, we need to express \( 920.7 \) in scientific notation. We can write \( 920.7 \) as:
\[ 920.7 = 9.207 \times 10^2 \]
Therefore, we can rewrite the total weight as:
\[ \text{Total weight} = 9.207 \times 10^2 \times 10^{-5} \]
Now we combine the powers of ten:
\[ = 9.207 \times 10^{2 - 5} \] \[ = 9.207 \times 10^{-3} , \text{grams} \]
Thus, the weight of the original sample, expressed in scientific notation, is:
\[ \boxed{9.207 \times 10^{-3}} , \text{grams} \]
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