Answer :
To multiply numbers in scientific notation, we follow these steps:
1. Multiply the coefficients:
Multiply the numbers in front of the powers of 10. Here, we have
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents:
When multiplying powers of 10, we add their exponents. We have
[tex]$$10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4.$$[/tex]
3. Combine the results:
This gives an intermediate product:
[tex]$$36.9 \times 10^4.$$[/tex]
4. Normalize the answer:
In standard scientific notation, the coefficient must be between 1 and 10. The coefficient [tex]$36.9$[/tex] can be rewritten as
[tex]$$36.9 = 3.69 \times 10^1.$$[/tex]
Substituting this into the intermediate product yields:
[tex]$$36.9 \times 10^4 = (3.69 \times 10^1) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Thus, the final answer in scientific notation is
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]
1. Multiply the coefficients:
Multiply the numbers in front of the powers of 10. Here, we have
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents:
When multiplying powers of 10, we add their exponents. We have
[tex]$$10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4.$$[/tex]
3. Combine the results:
This gives an intermediate product:
[tex]$$36.9 \times 10^4.$$[/tex]
4. Normalize the answer:
In standard scientific notation, the coefficient must be between 1 and 10. The coefficient [tex]$36.9$[/tex] can be rewritten as
[tex]$$36.9 = 3.69 \times 10^1.$$[/tex]
Substituting this into the intermediate product yields:
[tex]$$36.9 \times 10^4 = (3.69 \times 10^1) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Thus, the final answer in scientific notation is
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]
