To determine the equivalent measurement in inches for one thousand microns, we start by understanding the conversion factor provided. One micron is equivalent to [tex]\(3.937 \times 10^{-5}\)[/tex] inch.
To find how many inches one thousand microns correspond to, we simply multiply the conversion factor for one micron by one thousand.
Step-by-step, it can be shown as:
1. One micron equals [tex]\(3.937 \times 10^{-5}\)[/tex] inch.
2. To find the equivalent inches for one thousand microns, we perform the following multiplication:
[tex]\[
1000 \text{ microns} \times 3.937 \times 10^{-5} \text{ inch per micron}
\][/tex]
3. Begin by multiplying 1000 (representing the microns) by the numerical part of the conversion factor, 3.937:
[tex]\[
1000 \times 3.937 = 3937
\][/tex]
4. Next, incorporate the exponent [tex]\(10^{-5}\)[/tex] by multiplying the result (3937) by [tex]\(10^{-5}\)[/tex]:
[tex]\[
3937 \times 10^{-5}
\][/tex]
Thus, the equivalent measurement of one thousand microns in inches is [tex]\(3937 \times 10^{-5}\)[/tex] inch.
Since this expression matches one of the given answer choices, the correct answer is:
[tex]\[ \boxed{3937 \times 10^{-5}} \][/tex]
