Answer :
To multiply two numbers in scientific notation, we follow these steps:
1. Multiply the coefficients.
2. Add the exponents.
3. Normalize the result so that the coefficient is between 1 and 10.
Step 1: Multiply the coefficients
The coefficients are 8.2 and 4.5. Their product is
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
Step 2: Add the exponents
The exponents are 9 and -5. Their sum is
[tex]$$9 + (-5) = 4.$$[/tex]
Thus, we have the initial result as
[tex]$$36.9 \times 10^4.$$[/tex]
Step 3: Normalize the result
The coefficient 36.9 is not between 1 and 10. We can write
[tex]$$36.9 = 3.69 \times 10.$$[/tex]
Substitute this in the product:
[tex]$$36.9 \times 10^4 = (3.69 \times 10) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Therefore, the product of [tex]$8.2 \times 10^9$[/tex] and [tex]$4.5 \times 10^{-5}$[/tex] in scientific notation is
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]
1. Multiply the coefficients.
2. Add the exponents.
3. Normalize the result so that the coefficient is between 1 and 10.
Step 1: Multiply the coefficients
The coefficients are 8.2 and 4.5. Their product is
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
Step 2: Add the exponents
The exponents are 9 and -5. Their sum is
[tex]$$9 + (-5) = 4.$$[/tex]
Thus, we have the initial result as
[tex]$$36.9 \times 10^4.$$[/tex]
Step 3: Normalize the result
The coefficient 36.9 is not between 1 and 10. We can write
[tex]$$36.9 = 3.69 \times 10.$$[/tex]
Substitute this in the product:
[tex]$$36.9 \times 10^4 = (3.69 \times 10) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Therefore, the product of [tex]$8.2 \times 10^9$[/tex] and [tex]$4.5 \times 10^{-5}$[/tex] in scientific notation is
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]