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2. [tex]\(\sqrt{2}\)[/tex] as a decimal is approximately 1.4142. Using this decimal, find the first four decimal places of the answer to the long division problem. (Show your work.)

[tex]\[
\sqrt{2} \div 1.000 = 1.4142 \div 1.000 =
\][/tex]


Sagot :

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]