Question
4.1 × 10^3
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
1.64 × 10^4
4.1 × 10^8
4.1 × 10^3
16.4 × 10^3
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
1.64 × 10^4
4.1 × 10^8
4.1 × 10^3
16.4 × 10^3
Answers
GPT-4o mini
To find the number of bacteria in a sample weighing 4 grams, we can use the proportion based on the information given for the 1 gram sample.
1. Start with the number of bacteria in 1 gram:
\[
4.1 \times 10^3 \text{ bacteria}
\]
2. To find the number of bacteria in 4 grams, we multiply by 4:
\[
\text{Number of bacteria in 4 grams} = 4 \times (4.1 \times 10^3)
\]
3. Perform the multiplication:
\[
4 \times 4.1 = 16.4
\]
4. So, multiplying gives:
\[
16.4 \times 10^3
\]
5. To express this in proper scientific notation, we need to adjust it to have only one non-zero digit to the left of the decimal. We can do this by converting \(16.4\) into \(1.64\) and increasing the exponent by 1:
\[
16.4 \times 10^3 = 1.64 \times 10^4
\]
Therefore, the number of bacteria in a 4 gram sample is:
\[
\boxed{1.64 \times 10^4}
\]
1. Start with the number of bacteria in 1 gram:
\[
4.1 \times 10^3 \text{ bacteria}
\]
2. To find the number of bacteria in 4 grams, we multiply by 4:
\[
\text{Number of bacteria in 4 grams} = 4 \times (4.1 \times 10^3)
\]
3. Perform the multiplication:
\[
4 \times 4.1 = 16.4
\]
4. So, multiplying gives:
\[
16.4 \times 10^3
\]
5. To express this in proper scientific notation, we need to adjust it to have only one non-zero digit to the left of the decimal. We can do this by converting \(16.4\) into \(1.64\) and increasing the exponent by 1:
\[
16.4 \times 10^3 = 1.64 \times 10^4
\]
Therefore, the number of bacteria in a 4 gram sample is:
\[
\boxed{1.64 \times 10^4}
\]