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Express 8/11

as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)

3 answers

To express \( \frac{8}{11} \) as a repeating decimal, we can perform long division.

  1. Dividing 8 by 11:
    • 11 goes into 8, 0 times.
    • Place a decimal point and add a zero, making it 80.
    • 11 goes into 80, 7 times (since \( 11 \times 7 = 77 \)).
    • Subtract 77 from 80 to get a remainder of 3.
    • Bring down another zero, making it 30.
    • 11 goes into 30, 2 times (since \( 11 \times 2 = 22 \)).
    • Subtract 22 from 30 to get a remainder of 8.

At this point, we notice that we are back to the remainder of 8, which is where we started.

Thus, the decimal representation begins to repeat with the digits 72.

Putting it all together, we find that: \[ \frac{8}{11} = 0.\overline{72} \] This means the repeating decimal is \( 0.727272...\), and we mark the repeating part with a bar as \( 0.\overline{72} \).

simple

Sure!

To express \( \frac{8}{11} \) as a repeating decimal:

  1. Divide 8 by 11:
    • \( 8 \div 11 = 0.727272... \)

So, you can write it as:

\[ \frac{8}{11} = 0.\overline{72} \]

The \( \overline{72} \) indicates that "72" is the repeating part.