4.1 × 103 bacteria are measured in a sand sample that weights 1 gram. Express in scientific notation the amount of bacteria in a sample weighing 4 grams. Show your work. (1 point) Responses 4.1 × 103 4.1 × 103 4.1 × 108 4.1 × 108 16.4 × 103 16.4 × 103 1.64 × 104

Answer 1

To find the amount of bacteria in a sample weighing 4 grams, we can use the bacteria count from the 1 gram sample and scale it up.

1. The number of bacteria in 1 gram of sand is given as \(4.1 \times 10^3\).
2. To find the number of bacteria in 4 grams, we multiply by 4:

\[ 4 \times (4.1 \times 10^3) \]

3. Performing the multiplication:

\[ 4 \times 4.1 = 16.4 \]

So we now have:

\[ 16.4 \times 10^3 \]

4. However, scientific notation requires that we express this in a specific format (a number between 1 and 10 multiplied by a power of 10). Therefore, we convert \(16.4\) into proper scientific notation:

\[ 16.4 = 1.64 \times 10^1 \]

5. Now we combine the powers of 10:

\[ 16.4 \times 10^3 = (1.64 \times 10^1) \times 10^3 = 1.64 \times 10^{1+3} = 1.64 \times 10^4 \]

Thus, the amount of bacteria in a sample weighing 4 grams is \(1.64 \times 10^4\).

The correct response is:

1.64 × 10^4