Express 7/11 as a repeating decimal. Mark the cycle of repeating digits with a bar. Note: You will find the option to add a bar above text in the Geometry ( ∠ ) keyboard.

Answer 1

To express \( \frac{7}{11} \) as a repeating decimal, we can perform long division.

1. Divide 7 by 11.

   • 11 goes into 70 six times (6 * 11 = 66).
   • Subtract 66 from 70, giving a remainder of 4.
   • Bring down a 0 (making it 40).

2. Then, divide 40 by 11.

   • 11 goes into 40 three times (3 * 11 = 33).
   • Subtract 33 from 40, giving a remainder of 7.
   • Bring down another 0 (making it 70).

3. Now, you'll notice you're back to the division of 70, which we've already calculated (6), leading us back into the repeating cycle.

This means the decimal representation of \( \frac{7}{11} \) is:

\[ 0.636363\ldots \]

We can indicate the repeating portion with a bar:

\[ 0.\overline{63} \]