To determine the amount of bacteria in a sand sample that weighs 4 grams, we start with the given value for a 1-gram sample:
- The number of bacteria in a 1-gram sample is \(4.1 \times 10^3\) bacteria.
To calculate the amount of bacteria in a 4-gram sand sample, we multiply the number of bacteria in 1 gram by 4:
\[ \text{Number of bacteria in 4 grams} = 4 \times (4.1 \times 10^3) \]
Now, we perform the multiplication:
\[ = 4 \times 4.1 \times 10^3 \]
Calculating \(4 \times 4.1\):
\[ 4 \times 4.1 = 16.4 \]
Now, combine this with the \(10^3\):
\[ = 16.4 \times 10^3 \]
Finally, we express this result in proper scientific notation. The value \(16.4\) can be rewritten as \(1.64 \times 10^1\):
\[ 16.4 \times 10^3 = (1.64 \times 10^1) \times 10^3 \]
Using the laws of exponents, we can combine the powers of ten:
\[ = 1.64 \times 10^{1+3} \] \[ = 1.64 \times 10^4 \]
Thus, the amount of bacteria in a 4-gram sample is:
\[ \boxed{1.64 \times 10^4} \]
1 answer