Let's go through this problem step-by-step to understand how to evaluate the given factors involving multiplication by [tex]\(10^{16}\)[/tex].
1. Identify the factors:
We have two factors for our multiplication operation:
- The first factor is [tex]\( 1.234 \)[/tex].
- The second factor is [tex]\( 10^{16} \)[/tex].
2. Understanding the multiplication:
When we multiply a number by [tex]\(10^{16}\)[/tex], we are essentially shifting the decimal point 16 places to the right. This is the same as multiplying by 10,000,000,000,000,000 (which is 1 followed by sixteen zeroes).
3. Perform the multiplication:
- Let's multiply the factor [tex]\(1.234\)[/tex] by [tex]\(10^{16}\)[/tex].
To visualize, [tex]\(1.234\)[/tex] moves the decimal point 16 places to the right:
[tex]\(1.234\)[/tex] becomes [tex]\(12,340,000,000,000,000\)[/tex].
4. Express the result:
In scientific notation, shifting the decimal point 16 places to the right converts [tex]\(1.234\)[/tex] into [tex]\(1.234 \times 10^{16}\)[/tex].
5. Presenting the result:
The problem's multiplication of [tex]\(1.234\)[/tex] by [tex]\(10^{16}\)[/tex] gives us:
- The factors are [tex]\(1.234\)[/tex] and [tex]\(10^{16}\)[/tex].
- The product (result of the multiplication) is [tex]\(1.234 \times 10^{16}\)[/tex], which can be written as [tex]\(1.234e+16\)[/tex] in scientific notation.
Thus, the product of multiplying [tex]\(1.234\)[/tex] by [tex]\(10^{16}\)[/tex] is [tex]\(1.234 \times 10^{16}\)[/tex] or [tex]\(1.234e+16\)[/tex].
