To find the amount of bacteria in a sample weighing 4 grams based on the measurement of \(4.1 \times 10^3\) bacteria in 1 gram, you can use a proportional relationship.
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Amount of bacteria per gram:
- You have \(4.1 \times 10^3\) bacteria in 1 gram.
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Calculating for 4 grams:
- To find the amount of bacteria in 4 grams, multiply the amount in 1 gram by 4: \[ \text{Amount of bacteria in 4 grams} = 4 \times (4.1 \times 10^3) \]
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Perform the multiplication: \[ 4 \times (4.1) = 16.4 \] Thus: \[ \text{Amount of bacteria in 4 grams} = 16.4 \times 10^3 \]
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Express in scientific notation:
- The number \(16.4\) can be expressed in scientific notation as \(1.64 \times 10^1\).
- Now, combine this with \(10^3\): \[ 16.4 \times 10^3 = (1.64 \times 10^1) \times 10^3 = 1.64 \times 10^{1 + 3} = 1.64 \times 10^4 \]
Thus, the amount of bacteria in a sample weighing 4 grams is: \[ \boxed{1.64 \times 10^4} \]
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