To find the expected number of bacteria in a cubic yard of compost, we first need to use the information provided: 1 gram of compost contains approximately \(1.1 \times 10^9\) bacteria.
Given that one cubic yard of compost has a mass of about 765,000 grams, we can calculate the total number of bacteria in one cubic yard by multiplying the number of bacteria per gram by the total mass in grams:
\[ \text{Total bacteria} = \text{bacteria per gram} \times \text{mass in grams} \] \[ \text{Total bacteria} = (1.1 \times 10^9) \times 765,000 \]
Now we perform the multiplication: \[ 765,000 = 7.65 \times 10^5 \] \[ \text{Total bacteria} = (1.1 \times 10^9) \times (7.65 \times 10^5) \]
When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents: \[ = (1.1 \times 7.65) \times 10^{9 + 5} \] \[ = 8.415 \times 10^{14} \]
Thus, the expected number of bacteria in one cubic yard of compost is approximately: \[ \boxed{8.4 \times 10^{14}} \]
3 answers