To determine how much thicker the human hair is compared to the piece of paper, we need to follow these steps:
1. Convert the measurements to decimal form:
- The diameter of the human hair is [tex]\(3.15 \times 10^{-2}\)[/tex] inches.
- The thickness of the piece of paper is [tex]\(3.94 \times 10^{-3}\)[/tex] inches.
Converting these values to decimal form:
- Hair diameter: [tex]\(0.0315\)[/tex] inches
- Paper thickness: [tex]\(0.00394\)[/tex] inches
2. Calculate the difference in thickness:
- Subtract the thickness of the piece of paper from the diameter of the human hair:
[tex]\[
\text{Difference} = 0.0315 - 0.00394 = 0.02756 \text{ inches}
\][/tex]
3. Convert the difference to scientific notation:
- The result from our subtraction is [tex]\(0.02756\)[/tex] inches.
- To convert [tex]\(0.02756\)[/tex] to scientific notation, we observe that [tex]\(0.02756\)[/tex] can be written as [tex]\(2.756 \times 10^{-2}\)[/tex] however, in the given results, we round to two decimal places for consistency:
[tex]\[
0.02756 \approx 2.76 \times 10^{-2}
\][/tex]
Hence, the difference in thickness between the human hair and the piece of paper, in scientific notation, is [tex]\(2.76 \times 10^{-2}\)[/tex] inches.
Therefore, the correct answer is:
[tex]\[
7.9 \times 10^{-2} \text{ inches}
\][/tex]
