Let's work through the problem step-by-step.
1. We need to divide [tex]\(1.0000\)[/tex] by approximately [tex]\(\sqrt{2}\)[/tex], which is given as [tex]\(1.4142\)[/tex].
2. Perform the long division:
[tex]\[
1.4142 \div 1.0000
\][/tex]
3. The quotient of the division [tex]\(1.0000 \div 1.4142\)[/tex] is approximately [tex]\(0.7071\)[/tex].
4. To determine the first four decimal places of this quotient:
[tex]\[
0.7071~~~~
\][/tex]
Thus, the first four decimal places of the answer to the long division problem [tex]\( \sqrt{2} \)[/tex] divided by [tex]\(1.0000\)[/tex] using the approximate value of [tex]\(1.4142\)[/tex] are:
[tex]\[
0.7071
\][/tex]
