To solve for the scientific notation of 37.8%, follow these step-by-step instructions:
1. Convert the percentage to a decimal:
- We start by converting the given percentage, 37.8%, to a decimal.
- To do this, divide 37.8 by 100 (since 1% is equivalent to 1/100 or 0.01).
[tex]\[
37.8\% = \frac{37.8}{100} = 0.378
\][/tex]
2. Express the decimal in scientific notation:
- In scientific notation, we express a number in the form [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
- For the decimal 0.378, we need to express it in the form [tex]\( a \times 10^n \)[/tex].
- To convert 0.378 to scientific notation, identify [tex]\( a \)[/tex] and [tex]\( n \)[/tex]:
[tex]\[
0.378 = 3.78 \times 10^{-1}
\][/tex]
- Here, [tex]\( a = 3.78 \)[/tex] and [tex]\( n = -1 \)[/tex].
3. Identify the corresponding option:
- We are provided with several options, and we need to match our result to one of them:
[tex]\[
\text{A. } 3.78 \times 10^1 \\
\text{B. } 3.78 \times 10^{-2} \\
\text{C. } 3.78 \times 10^2 \\
\text{D. } 3.78 \times 10^{-1} \\
\text{E. } 3.78 \times 10^3
\][/tex]
- Comparing these options, the scientific notation we found, [tex]\( 3.78 \times 10^{-1} \)[/tex], matches option D.
Thus, the correct answer is:
[tex]\[
\boxed{3.78 \times 10^{-1}}
\][/tex]
