Question

Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)

Answer 1

where does the bar go?

Answer 2

what is the bar called?

Answer 3

To convert the fraction \( \frac{8}{11} \) into a repeating decimal, we can perform long division.

1. Divide 8 by 11. Since 8 is less than 11, we start with 0.
2. We add a decimal point and a zero, making it 80.
3. 11 goes into 80 seven times (since \( 11 \times 7 = 77 \)).
4. Subtract 77 from 80, which leaves us with 3.
5. Bring down another zero, making it 30.
6. 11 goes into 30 two times (since \( 11 \times 2 = 22 \)).
7. Subtract 22 from 30, which leaves us with 8.

Notice that we are back at the beginning, and this process will repeat indefinitely.

Thus, the decimal representation of \( \frac{8}{11} \) is:

\[
0.\overline{72}
\]

The repeating part is \( 72 \).

Answer 4

The bar should be placed over the digits that are repeating. For the fraction \( \frac{8}{11} \), which converts to the decimal \( 0.727272\ldots \), the bar should go over the "72" to indicate that these digits repeat indefinitely.

So, it should be expressed as:

\[
0.\overline{72}
\]

This notation shows that "72" is the repeating part of the decimal.

Answer 5

The bar placed over the repeating digits in a decimal is called a **vinculum**. It indicates that the digits underneath the bar repeat indefinitely. For example, in the notation \( 0.\overline{72} \), the vinculum signifies that the digits "72" repeat continuously.