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Answer :
To compute the product of
[tex]$$8.2 \times 10^9$$[/tex]
and
[tex]$$4.5 \times 10^{-5},$$[/tex]
we can follow these steps:
1. Multiply the coefficients:
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents of the powers of 10:
[tex]$$9 + (-5) = 4.$$[/tex]
This gives an initial result of:
[tex]$$36.9 \times 10^4.$$[/tex]
3. Write the answer in proper scientific notation (where the coefficient must be between 1 and 10). Since [tex]$36.9$[/tex] is not between 1 and 10, we can express it as:
[tex]$$36.9 = 3.69 \times 10^1.$$[/tex]
4. Substitute this back into the product:
[tex]$$36.9 \times 10^4 = \left(3.69 \times 10^1\right) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Thus, the product in scientific notation is:
[tex]$$3.69 \times 10^5.$$[/tex]
[tex]$$8.2 \times 10^9$$[/tex]
and
[tex]$$4.5 \times 10^{-5},$$[/tex]
we can follow these steps:
1. Multiply the coefficients:
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]
2. Add the exponents of the powers of 10:
[tex]$$9 + (-5) = 4.$$[/tex]
This gives an initial result of:
[tex]$$36.9 \times 10^4.$$[/tex]
3. Write the answer in proper scientific notation (where the coefficient must be between 1 and 10). Since [tex]$36.9$[/tex] is not between 1 and 10, we can express it as:
[tex]$$36.9 = 3.69 \times 10^1.$$[/tex]
4. Substitute this back into the product:
[tex]$$36.9 \times 10^4 = \left(3.69 \times 10^1\right) \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]
Thus, the product in scientific notation is:
[tex]$$3.69 \times 10^5.$$[/tex]
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