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:
- Start by multiplying the two numbers in front of the powers of ten: [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
- [tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Multiply the Powers of Ten:
- For the powers of ten, apply the rule of exponents, which states that [tex]\((10^a) \times (10^b) = 10^{a+b}\)[/tex].
- Here we have [tex]\(10^9\)[/tex] and [tex]\(10^{-5}\)[/tex], so add the exponents: [tex]\(9 + (-5) = 4\)[/tex].
3. Combine the Results:
- Combine the product of the coefficients with the product of the powers of ten.
- This gives us [tex]\(36.9 \times 10^4\)[/tex].
4. Convert to Proper Scientific Notation:
- In scientific notation, we usually want the coefficient to be between 1 and 10.
- Convert [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] by moving the decimal point one place to the left, and adjust the power of ten by adding 1 to the exponent to compensate.
- Thus, [tex]\(36.9 \times 10^4\)[/tex] becomes [tex]\(3.69 \times 10^5\)[/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]\(3.69 \times 10^5\)[/tex].
1. Multiply the Coefficients:
- Start by multiplying the two numbers in front of the powers of ten: [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
- [tex]\(8.2 \times 4.5 = 36.9\)[/tex].
2. Multiply the Powers of Ten:
- For the powers of ten, apply the rule of exponents, which states that [tex]\((10^a) \times (10^b) = 10^{a+b}\)[/tex].
- Here we have [tex]\(10^9\)[/tex] and [tex]\(10^{-5}\)[/tex], so add the exponents: [tex]\(9 + (-5) = 4\)[/tex].
3. Combine the Results:
- Combine the product of the coefficients with the product of the powers of ten.
- This gives us [tex]\(36.9 \times 10^4\)[/tex].
4. Convert to Proper Scientific Notation:
- In scientific notation, we usually want the coefficient to be between 1 and 10.
- Convert [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] by moving the decimal point one place to the left, and adjust the power of ten by adding 1 to the exponent to compensate.
- Thus, [tex]\(36.9 \times 10^4\)[/tex] becomes [tex]\(3.69 \times 10^5\)[/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]\(3.69 \times 10^5\)[/tex].