# Evaluate the quotient and express the answer as a repeating decimal--showing the repeating pattern twice: 1 ÷ 7 = _____?????

May 18, 2018

$0.142857142857$

#### Explanation:

By evaluate the quotient, the problem simply means to complete the division.

$\frac{1}{7} = 0.142857142857142857$

Now, we need to identify the repeating decimal.

$0 . \textcolor{red}{142857} \textcolor{g r e e n}{142857} \textcolor{\in \mathrm{di} g o}{142857}$

Therefore, the pattern is $142857$. In the approximated solution above, it repeats $3$ times. However, it would actually continue on infinitely. But the problem asks for it to be repeated twice.

$0.142857142857$