Alright, let's convert the number [tex]\( 361.14 \times 10^8 \)[/tex] into correct scientific notation step-by-step.
1. Understand the Structure of Scientific Notation:
- Scientific notation is written as [tex]\( a \times 10^b \)[/tex], where [tex]\( a \)[/tex] (the coefficient) is a number greater than or equal to 1 and less than 10, and [tex]\( b \)[/tex] (the exponent) is an integer.
2. Identify the Current Number and Exponent:
- The number given is [tex]\( 361.14 \)[/tex], and it is multiplied by [tex]\( 10^8 \)[/tex].
3. Adjust the Coefficient to Fall Between 1 and 10:
- To convert [tex]\( 361.14 \)[/tex] to a number between 1 and 10, we need to express it as [tex]\( 3.6114 \times 10^2 \)[/tex], because [tex]\( 361.14 = 3.6114 \times 100 \)[/tex].
4. Combine the Exponents:
- Originally, the number was [tex]\( 361.14 \times 10^8 \)[/tex].
- We have converted [tex]\( 361.14 \)[/tex] to [tex]\( 3.6114 \times 10^2 \)[/tex] as the coefficient.
- So, the new expression is [tex]\( 3.6114 \times 10^2 \times 10^8 \)[/tex].
5. Simplify the Exponent:
- Combine the exponents [tex]\( 10^2 \)[/tex] and [tex]\( 10^8 \)[/tex]:
[tex]\( 10^2 \times 10^8 = 10^{2+8} = 10^{10} \)[/tex].
6. Final Scientific Notation:
- Thus, the converted form is [tex]\( 3.6114 \times 10^{10} \)[/tex].
Therefore, the correct scientific notation for [tex]\( 361.14 \times 10^8 \)[/tex] is [tex]\( \boxed{3.6114} \times 10^{\boxed{10}} \)[/tex].
