To calculate the total amount of trash thrown away in the United States in 2013, you can multiply the average amount of trash thrown away per person per day by the number of people and then by the number of days in a year.
Given:
- Average trash per person per day: \( 4.5 \times 10^2 \) grams
- Number of people: \( 3.2 \times 10^6 \) people
- Number of days in a year: 365
First, let's multiply the amount of trash per person by the population:
\[ (4.5 \times 10^2 \text{ grams}) \times (3.2 \times 10^6 \text{ people}) \]
Using the properties of exponents, we can rearrange the multiplication:
\[ = 4.5 \times 3.2 \times 10^{2 + 6} \]
Calculating \( 4.5 \times 3.2 \):
\[ 4.5 \times 3.2 = 14.4 \]
Now combining everything:
\[ = 14.4 \times 10^8 \text{ grams} \]
Next, we need to include the number of days in a year:
\[ 14.4 \times 10^8 \text{ grams/day} \times 365 \text{ days} \]
Now let's convert \( 365 \) into scientific notation. This is approximately \( 3.65 \times 10^2 \).
Now multiplying:
\[ (14.4 \times 10^8) \times (3.65 \times 10^2) \]
Again, applying the properties of exponents:
\[ = 14.4 \times 3.65 \times 10^{8 + 2} \]
Now we calculate \( 14.4 \times 3.65 \):
\[ 14.4 \times 3.65 \approx 52.680 \]
So we have:
\[ = 52.680 \times 10^{10} \]
To express this in proper scientific notation, we convert \( 52.680 \) into \( 5.2680 \) by moving the decimal point one place to the left, which increases the exponent by 1:
\[ = 5.2680 \times 10^{11} \]
For simplicity, we can round this to:
\[ \approx 5.3 \times 10^{11} \]
Thus, the final answer can be expressed as:
5.3 x 10 __ G (where the blank is 11).