Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex], let's proceed step by step:
1. Multiply the base numbers:
[tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Combine the powers of ten:
When multiplying numbers in scientific notation, you add the exponents of the powers of ten.
So, [tex]\(10^9 \times 10^{-5}\)[/tex] equals [tex]\(10^{9 + (-5)} = 10^{4}\)[/tex].
3. Express the result in scientific notation:
The product of the base numbers is 36.9, and you have [tex]\(10^4\)[/tex] from the powers of ten.
So, the product in scientific notation is [tex]\(36.9 \times 10^4\)[/tex].
4. Adjust to proper scientific notation:
In proper scientific notation, the number should be a value between 1 and 10, followed by a power of ten.
So, [tex]\(36.9 \times 10^4\)[/tex] can be written as [tex]\(3.69 \times 10^5\)[/tex] (by moving the decimal one place to the left and increasing the exponent by 1).
Therefore, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] is [tex]\(3.69 \times 10^5\)[/tex].
1. Multiply the base numbers:
[tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Combine the powers of ten:
When multiplying numbers in scientific notation, you add the exponents of the powers of ten.
So, [tex]\(10^9 \times 10^{-5}\)[/tex] equals [tex]\(10^{9 + (-5)} = 10^{4}\)[/tex].
3. Express the result in scientific notation:
The product of the base numbers is 36.9, and you have [tex]\(10^4\)[/tex] from the powers of ten.
So, the product in scientific notation is [tex]\(36.9 \times 10^4\)[/tex].
4. Adjust to proper scientific notation:
In proper scientific notation, the number should be a value between 1 and 10, followed by a power of ten.
So, [tex]\(36.9 \times 10^4\)[/tex] can be written as [tex]\(3.69 \times 10^5\)[/tex] (by moving the decimal one place to the left and increasing the exponent by 1).
Therefore, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] is [tex]\(3.69 \times 10^5\)[/tex].