Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, follow these steps:
1. Multiply the coefficients:
- Multiply 8.2 and 4.5.
- [tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Combine the powers of 10:
- Use the rule for multiplying powers with the same base, which states that you add the exponents.
- [tex]\(10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4\)[/tex].
3. Combine the results:
- Multiply the product of the coefficients (36.9) by the combined power of 10 ([tex]\(10^4\)[/tex]).
- So, [tex]\(36.9 \times 10^4\)[/tex].
4. Express in scientific notation:
- To properly express the result in scientific notation, adjust the decimal point so that there is one non-zero digit to the left of it.
- This gives us [tex]\(3.69 \times 10^5\)[/tex].
Given the options:
- [tex]$36.9 \times 10^{-45}$[/tex]
- [tex]$12.7 \times 10^4$[/tex]
- [tex]$3.69 \times 10^5$[/tex]
- [tex]$3.69 \times 10^{14}$[/tex]
The correct answer is [tex]\(3.69 \times 10^5\)[/tex].
1. Multiply the coefficients:
- Multiply 8.2 and 4.5.
- [tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Combine the powers of 10:
- Use the rule for multiplying powers with the same base, which states that you add the exponents.
- [tex]\(10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4\)[/tex].
3. Combine the results:
- Multiply the product of the coefficients (36.9) by the combined power of 10 ([tex]\(10^4\)[/tex]).
- So, [tex]\(36.9 \times 10^4\)[/tex].
4. Express in scientific notation:
- To properly express the result in scientific notation, adjust the decimal point so that there is one non-zero digit to the left of it.
- This gives us [tex]\(3.69 \times 10^5\)[/tex].
Given the options:
- [tex]$36.9 \times 10^{-45}$[/tex]
- [tex]$12.7 \times 10^4$[/tex]
- [tex]$3.69 \times 10^5$[/tex]
- [tex]$3.69 \times 10^{14}$[/tex]
The correct answer is [tex]\(3.69 \times 10^5\)[/tex].