To find the total amount of trash thrown away in the United States in 2013, we can multiply the average amount of trash thrown away per person per day by the total number of people, and then by the number of days in a year.
- The average amount of trash per person per day is given as \(4.5 \times 10^2\) grams.
- The population in 2013 is given as \(3.2 \times 10^6\) people.
- There are 365 days in a year.
Now, we can set up the calculation:
\[ \text{Total trash} = (\text{trash per person per day}) \times (\text{number of people}) \times (\text{number of days in a year}) \]
Substituting the values, we get:
\[ \text{Total trash} = (4.5 \times 10^2 \text{ grams}) \times (3.2 \times 10^6 \text{ people}) \times (365 \text{ days}) \]
Now, we'll compute this step by step:
First, compute the product of the grams and the number of people:
\[ 4.5 \times 10^2 \times 3.2 \times 10^6 = (4.5 \times 3.2) \times (10^2 \times 10^6) = 14.4 \times 10^{2 + 6} = 14.4 \times 10^8 \]
Next, we'll multiply by the number of days in a year:
\[ 14.4 \times 10^8 \times 365 \]
We can first calculate \(14.4 \times 365\):
\[ 14.4 \times 365 = 5256 \]
Thus,
\[ 14.4 \times 10^8 \times 365 = 5256 \times 10^8 = 5.256 \times 10^{11} \]
Therefore, the total amount of trash thrown away in the United States in 2013 is approximately:
\[ \boxed{5.256 \times 10^{11}} \text{ grams} \]