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Answer :
To find the product of
$$8.2 \times 10^9 \quad \text{and} \quad 4.5 \times 10^{-5},$$
follow these steps:
1. **Multiply the coefficients:**
Multiply $8.2$ and $4.5$:
$$8.2 \times 4.5 = 36.9.$$
2. **Add the exponents:**
Add the exponents $9$ and $-5$:
$$9 + (-5) = 4.$$
3. **Combine the results:**
Initially, the product is written as:
$$36.9 \times 10^4.$$
4. **Normalize the result in scientific notation:**
In proper scientific notation, the coefficient should be in the range $[1,10)$. Since $36.9$ is greater than $10$, express it as:
$$36.9 = 3.69 \times 10.$$
Replace back into the expression:
$$36.9 \times 10^4 = 3.69 \times 10 \times 10^4.$$
Combine the powers of $10$:
$$3.69 \times 10^{1+4} = 3.69 \times 10^5.$$
Thus, the product in proper scientific notation is:
$$\boxed{3.69 \times 10^5}.$$
$$8.2 \times 10^9 \quad \text{and} \quad 4.5 \times 10^{-5},$$
follow these steps:
1. **Multiply the coefficients:**
Multiply $8.2$ and $4.5$:
$$8.2 \times 4.5 = 36.9.$$
2. **Add the exponents:**
Add the exponents $9$ and $-5$:
$$9 + (-5) = 4.$$
3. **Combine the results:**
Initially, the product is written as:
$$36.9 \times 10^4.$$
4. **Normalize the result in scientific notation:**
In proper scientific notation, the coefficient should be in the range $[1,10)$. Since $36.9$ is greater than $10$, express it as:
$$36.9 = 3.69 \times 10.$$
Replace back into the expression:
$$36.9 \times 10^4 = 3.69 \times 10 \times 10^4.$$
Combine the powers of $10$:
$$3.69 \times 10^{1+4} = 3.69 \times 10^5.$$
Thus, the product in proper scientific notation is:
$$\boxed{3.69 \times 10^5}.$$
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