To solve the expression [tex]\( \frac{1}{6} \)[/tex], follow these steps:
1. Understanding the Operation:
The expression involves dividing 1 by 6. Division can be interpreted as finding out how many times the divisor (6) fits into the dividend (1).
2. Setting Up the Division:
We need to determine the value of [tex]\( \frac{1}{6} \)[/tex].
3. Performing the Division:
[tex]\[
\begin{array}{r}
0.16666666666666666 \\
\hline
6 |1.00000000000000000 \\
\end{array}
\][/tex]
When 1 is divided by 6, the quotient is a repeating decimal, which means 6 does not fit into 1 evenly. We need to calculate how many times 6 fits into 10 (since we add decimal places to 1 to manage division) and repeat this process.
4. Interpreting the Result:
The result of dividing 1 by 6 is a repeating decimal value:
[tex]\[
0.16666666666666666\ldots
\][/tex]
This value means that the digit '6' repeats indefinitely.
5. Writing the Final Answer:
After performing the division, we conclude that:
[tex]\[
\frac{1}{6} = 0.16666666666666666
\][/tex]
Therefore, the value of [tex]\( \frac{1}{6} \)[/tex] is approximately [tex]\( 0.16666666666666666 \)[/tex], where the digit '6' repeats infinitely.
