To determine which decimal is closest in value to the fraction [tex]\(\frac{1}{6}\)[/tex], let's follow a step-by-step approach.
First, we need to convert the fraction [tex]\(\frac{1}{6}\)[/tex] to its decimal form. By performing the division [tex]\(1 \div 6\)[/tex], we get approximately:
[tex]\[
\frac{1}{6} \approx 0.1667
\][/tex]
Next, we compare this decimal value, [tex]\(0.1667\)[/tex], with the given choices to find the closest one. The choices are:
A. 0.75
B. 0.6
C. 0.1667
We can compute the absolute differences between [tex]\(0.1667\)[/tex] and each of the choices:
1. For choice A, [tex]\(0.75\)[/tex]:
[tex]\[
|0.1667 - 0.75| = |0.1667 - 0.75| = 0.5833
\][/tex]
2. For choice B, [tex]\(0.6\)[/tex]:
[tex]\[
|0.1667 - 0.6| = |0.1667 - 0.6| = 0.4333
\][/tex]
3. For choice C, [tex]\(0.1667\)[/tex]:
[tex]\[
|0.1667 - 0.1667| = |0.1667 - 0.1667| = 0.0
\][/tex]
Analyzing the absolute differences, we find that:
- The difference for choice A is [tex]\(0.5833\)[/tex].
- The difference for choice B is [tex]\(0.4333\)[/tex].
- The difference for choice C is [tex]\(0.0\)[/tex].
The smallest difference (which represents the closest value) is for choice C: [tex]\(0.1667\)[/tex].
Therefore, the decimal closest in value to the fraction [tex]\(\frac{1}{6}\)[/tex] is:
\[
\boxed{0.1667}
