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

Answer 1

To express the fraction 8/11 as a repeating decimal, we can use long division.

Starting with the division problem 8 ÷ 11:

0. followed by the repeating decimal part
11 | 8.000000…

We can see that 11 does not divide evenly into 8, so we bring down another digit, making it 80.

0. followed by the repeating decimal part
11 | 8.000000…
-0

Now, we divide 11 into 80:

0. followed by the repeating decimal part
11 | 8.000000…
-0
77
-----
30

Since 11 does not divide evenly into 30, we bring down another digit, making it 300.

0. followed by the repeating decimal part
11 | 8.000000…
-0
77
-----
30
-22
------
80
-77
------
30
-22
------
80
-77
-------
30
-22
-------
80
-77
--------
and so on...

As we can see, the division continues in a repeating pattern where the remainder cycles between 30, 22, 80, and 77.

Therefore, the decimal representation of 8/11 is 0. followed by the repeating decimal pattern 72, where the 72 cycles over and over.

So, 8/11 as a repeating decimal can be written as 0.72 with the bar over the 72.