Question: A single tree produces about $2.6 \times 10^{2}$ pounds of oxygen each year. The Amazon rainforest has about $3.9 \times 10^{11}$ trees.
About how many pounds of oxygen are produced in the Amazon rainforest per day?
Enter your answer by filling in the box.
$2.8 \times 10^{\square}$ pounds per day
1. **State the problem:** We want to find how many pounds of oxygen are produced per day by all the trees in the Amazon rainforest.
2. **Given data:**
- Oxygen produced by one tree per year: $2.6 \times 10^{2}$ pounds
- Number of trees in the Amazon: $3.9 \times 10^{11}$
3. **Calculate total oxygen produced per year by all trees:**
$$\text{Total per year} = (2.6 \times 10^{2}) \times (3.9 \times 10^{11})$$
4. **Multiply the coefficients and add exponents:**
$$2.6 \times 3.9 = 10.14$$
$$10^{2} \times 10^{11} = 10^{2+11} = 10^{13}$$
So,
$$\text{Total per year} = 10.14 \times 10^{13}$$
5. **Convert to scientific notation:**
$$10.14 \times 10^{13} = 1.014 \times 10^{1} \times 10^{13} = 1.014 \times 10^{14}$$
6. **Calculate oxygen produced per day:**
There are 365 days in a year, so
$$\text{Total per day} = \frac{1.014 \times 10^{14}}{365}$$
7. **Divide the coefficient:**
$$\frac{1.014}{365} \approx 0.00278$$
So,
$$\text{Total per day} = 0.00278 \times 10^{14}$$
8. **Convert to proper scientific notation:**
$$0.00278 = 2.78 \times 10^{-3}$$
Therefore,
$$\text{Total per day} = 2.78 \times 10^{-3} \times 10^{14} = 2.78 \times 10^{11}$$
9. **Round the coefficient to 2.8:**
$$\boxed{2.8 \times 10^{11}}$$ pounds per day.
**Final answer:** The Amazon rainforest produces about $2.8 \times 10^{11}$ pounds of oxygen per day.