Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, we can follow these steps:
1. Multiply the Coefficients:
- The coefficients (the numbers in front) are 8.2 and 4.5.
- First, multiply these coefficients:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the Exponents:
- The exponents are 9 and -5.
- To find the product's exponent, add these two exponents:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine Results in Scientific Notation:
- Use the product of the coefficients and the sum of the exponents to write the answer in scientific notation:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Adjust to Proper Scientific Notation:
- In proper scientific notation, the coefficient should be between 1 and 10. Here, [tex]\(36.9\)[/tex] is greater than 10.
- Adjust by moving the decimal one place to the left and increase the exponent by 1:
[tex]\[
3.69 \times 10^5
\][/tex]
Thus, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(3.69 \times 10^5\)[/tex].
1. Multiply the Coefficients:
- The coefficients (the numbers in front) are 8.2 and 4.5.
- First, multiply these coefficients:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the Exponents:
- The exponents are 9 and -5.
- To find the product's exponent, add these two exponents:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine Results in Scientific Notation:
- Use the product of the coefficients and the sum of the exponents to write the answer in scientific notation:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Adjust to Proper Scientific Notation:
- In proper scientific notation, the coefficient should be between 1 and 10. Here, [tex]\(36.9\)[/tex] is greater than 10.
- Adjust by moving the decimal one place to the left and increase the exponent by 1:
[tex]\[
3.69 \times 10^5
\][/tex]
Thus, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(3.69 \times 10^5\)[/tex].
