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Answer :
To find the product of
[tex]$$8.2 \times 10^9$$[/tex]
and
[tex]$$4.5 \times 10^{-5},$$[/tex]
follow these steps:
1. Multiply the coefficients:
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents for the powers of 10:
[tex]$$9 + (-5) = 4.$$[/tex]
So, the initial product is written as:
[tex]$$36.9 \times 10^4.$$[/tex]
3. The result must be in proper scientific notation, where the coefficient is between 1 and 10. The number [tex]$36.9$[/tex] is not in this range, so we normalize it. We express [tex]$36.9$[/tex] as:
[tex]$$36.9 = 3.69 \times 10.$$[/tex]
Substituting this back into the expression:
[tex]$$36.9 \times 10^4 = (3.69 \times 10) \times 10^4.$$[/tex]
4. Combine the powers of [tex]$10$[/tex]:
[tex]$$10 \times 10^4 = 10^{1+4} = 10^5.$$[/tex]
Thus, the product becomes:
[tex]$$3.69 \times 10^5.$$[/tex]
So, the product in scientific notation is:
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]
[tex]$$8.2 \times 10^9$$[/tex]
and
[tex]$$4.5 \times 10^{-5},$$[/tex]
follow these steps:
1. Multiply the coefficients:
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents for the powers of 10:
[tex]$$9 + (-5) = 4.$$[/tex]
So, the initial product is written as:
[tex]$$36.9 \times 10^4.$$[/tex]
3. The result must be in proper scientific notation, where the coefficient is between 1 and 10. The number [tex]$36.9$[/tex] is not in this range, so we normalize it. We express [tex]$36.9$[/tex] as:
[tex]$$36.9 = 3.69 \times 10.$$[/tex]
Substituting this back into the expression:
[tex]$$36.9 \times 10^4 = (3.69 \times 10) \times 10^4.$$[/tex]
4. Combine the powers of [tex]$10$[/tex]:
[tex]$$10 \times 10^4 = 10^{1+4} = 10^5.$$[/tex]
Thus, the product becomes:
[tex]$$3.69 \times 10^5.$$[/tex]
So, the product in scientific notation is:
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]
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