To convert the number [tex]\( 94.38 \times 10^2 \)[/tex] into scientific notation, follow these detailed steps:
1. Understanding the format: Scientific notation is a way of expressing numbers, typically in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq |a| < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
2. Initial number breakdown: The given number is [tex]\( 94.38 \times 10^2 \)[/tex].
3. Adjust the coefficient: To convert this to the standard form of scientific notation, we need to adjust [tex]\( 94.38 \)[/tex] such that it becomes a number between 1 and 10.
[tex]\[
94.38 \text{ can be written as } 9.438 \times 10^1 \text{ because shifting the decimal point one place to the left creates a number within the required range.}
\][/tex]
4. Combining the exponents: Since we have now expressed [tex]\( 94.38 \)[/tex] as [tex]\( 9.438 \times 10^1 \)[/tex], we need to incorporate the original [tex]\( \times 10^2 \)[/tex]:
[tex]\[
94.38 \times 10^2 = (9.438 \times 10^1) \times 10^2
\][/tex]
5. Adding the exponents: When we multiply powers of 10, we add their exponents. Thus,
[tex]\[
(9.438 \times 10^1) \times 10^2 = 9.438 \times 10^{1+2} = 9.438 \times 10^3
\][/tex]
6. Result: The number in the correct scientific notation form is [tex]\( 9.438 \times 10^3 \)[/tex].
Thus, the coefficient is [tex]\( 9.438 \)[/tex] (to be entered in the green box), and the exponent is [tex]\( 3 \)[/tex] (to be entered in the yellow box).
