To convert the number [tex]\( 94.38 \times 10^2 \)[/tex] into correct scientific notation, we need the coefficient to be a value between 1 and 10, and we want to adjust the exponent accordingly.
### Step-by-Step Solution:
1. Identify the given number and its current scientific notation:
- The given number is [tex]\( 94.38 \)[/tex] with an exponent of [tex]\( 2 \)[/tex].
2. Adjust the coefficient to be a value between 1 and 10:
- To achieve this, we divide [tex]\( 94.38 \)[/tex] by [tex]\( 10 \)[/tex], which gives us [tex]\( 9.438 \)[/tex].
- Of course, when we divide by [tex]\( 10 \)[/tex], since we are making the number smaller, we need to compensate by increasing the exponent by [tex]\( 1 \)[/tex].
3. Adjust the exponent:
- The original exponent is [tex]\( 2 \)[/tex].
- By making the coefficient ten times smaller, we increase the exponent by [tex]\( 1 \)[/tex], which results in the exponent moving from [tex]\( 2 \)[/tex] to [tex]\( 3 \)[/tex].
### Final Scientific Notation:
- The new coefficient is [tex]\( 9.438 \)[/tex].
- The new exponent is [tex]\( 3 \)[/tex].
Thus, the original number [tex]\( 94.38 \times 10^2 \)[/tex] in correct scientific notation is:
[tex]\[
9.438 \times 10^3
\][/tex]
So, the coefficient you should enter in the green box is [tex]\( 9.438 \)[/tex] and the exponent you should enter in the yellow box is [tex]\( 3 \)[/tex].
