To find the number of bacteria in a sample weighing 1818 grams, we can set up a ratio based on the known quantity of bacteria in the 11-gram sample.
Given:
- Number of bacteria in 11 grams = \( 5.8 \times 10^7 \)
- Weight of sample = 11 grams
First, we can calculate the number of bacteria per gram:
\[ \text{Bacteria per gram} = \frac{5.8 \times 10^7 \text{ bacteria}}{11 \text{ grams}} = \frac{5.8}{11} \times 10^7 \text{ bacteria/gram} \]
Calculating \( \frac{5.8}{11} \):
\[ \frac{5.8}{11} \approx 0.5273 \text{ (to four decimal places)} \]
Now, we can express this in scientific notation:
\[ 0.5273 \approx 5.273 \times 10^{-1} \]
Thus, the number of bacteria per gram is:
\[ 5.273 \times 10^{-1} \times 10^7 = 5.273 \times 10^{6} \text{ bacteria/gram} \]
Now, we can apply this to the 1818-gram sample:
\[ \text{Number of bacteria in 1818 grams} = 5.273 \times 10^6 \text{ bacteria/gram} \times 1818 \text{ grams} \]
Calculating \( 5.273 \times 1818 \):
\[ 5.273 \times 1818 \approx 9602.274 \]
Now we express this in scientific notation.
\[ 9602.274 \approx 9.602274 \times 10^3 \]
Now we need to convert this to an appropriate form. Since we are multiplying by \( 10^6 \), we can combine:
\[ 9.602274 \times 10^3 \times 10^6 = 9.602274 \times 10^{9} \]
Therefore, rounding to three significant figures, we can express the final number of bacteria in a sample weighing 1818 grams as:
\[ \approx 9.60 \times 10^9 \]
So, the final answer is:
\[ 9.60 \times 10^9 \text{ bacteria} \]
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