Answer :
Sure, let's find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation.
### Step-by-step solution:
1. Multiply the coefficients:
- The coefficients are [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
- Multiplying these together:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
- The exponents are [tex]\(9\)[/tex] and [tex]\(-5\)[/tex].
- Adding these together:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the result:
- The new coefficient is [tex]\(36.9\)[/tex].
- The new exponent is [tex]\(4\)[/tex].
So, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is:
[tex]\[
36.9 \times 10^4
\][/tex]
Now, let's match this with the given 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]\[
36.9 \times 10^4
\][/tex]
However, this option is not listed, so we need to convert [tex]\(36.9\)[/tex] to a number between 1 and 10, which changes the exponent.
[tex]\[ 36.9 \times 10^4 = 3.69 \times 10^5 \][/tex]
So the correct matching option is:
[tex]\[
3.69 \times 10^5
\][/tex]
### Step-by-step solution:
1. Multiply the coefficients:
- The coefficients are [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
- Multiplying these together:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
- The exponents are [tex]\(9\)[/tex] and [tex]\(-5\)[/tex].
- Adding these together:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the result:
- The new coefficient is [tex]\(36.9\)[/tex].
- The new exponent is [tex]\(4\)[/tex].
So, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is:
[tex]\[
36.9 \times 10^4
\][/tex]
Now, let's match this with the given 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]\[
36.9 \times 10^4
\][/tex]
However, this option is not listed, so we need to convert [tex]\(36.9\)[/tex] to a number between 1 and 10, which changes the exponent.
[tex]\[ 36.9 \times 10^4 = 3.69 \times 10^5 \][/tex]
So the correct matching option is:
[tex]\[
3.69 \times 10^5
\][/tex]