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.

Answer 1

To find the amount of bacteria in a 4-gram sample, we can multiply the number of bacteria in the 1-gram sample by 4.

Given that there are \(4.1 \times 10^3\) bacteria in 1 gram, the calculation for a 4-gram sample is:

\[ 4 \times (4.1 \times 10^3) = (4 \times 4.1) \times 10^3 = 16.4 \times 10^3 \]

Now we can express \(16.4 \times 10^3\) in proper scientific notation. To do this, we rewrite \(16.4\) as \(1.64 \times 10^1\):

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

Thus, the amount of bacteria in a sample weighing 4 grams is:

\[ \boxed{1.64 \times 10^4} \]