Question

Express 1/6 as a repeating decimal. Mark the cycle of the repeating digits with a bar¯¯¯¯¯¯¯

Answer 1

To express \( \frac{1}{6} \) as a repeating decimal, we can perform the division:

When you divide 1 by 6, you get:

- 1.00000...
- 6 goes into 10 once (1), leaving a remainder of 4.
- Bring down a 0 (making it 40).
- 6 goes into 40 six times (6), leaving a remainder of 4 again.
- Bring down another 0 (making it 40).
- This process repeats indefinitely.

The decimal representation of \( \frac{1}{6} \) is therefore \( 0.166666...\).

To indicate the repeating part, we can use a bar over the repeating digit(s):

\[
\frac{1}{6} = 0.1\overline{6}
\]

So, \( \frac{1}{6} \) expressed as a repeating decimal is \( 0.1\overline{6} \).