Express (8)/(11) as a repeating decimal. Mark the cycle of repeating digits with a bar.
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.
To express (8)/(11) as a repeating decimal, we can use long division:
11)8.000000...
- 7
---
10
- 9
---
10
- 9
---
10
The division goes on indefinitely with a repeating pattern of 9s. Therefore, (8)/(11) can be expressed as 0.727272... or 0.72¯¯¯¯¯.
To express the fraction (8)/(11) as a repeating decimal, we can perform long division. Here's how you can do it:
Step 1: Divide 8 by 11.
- The quotient is 0.
- Add a decimal point after the quotient, which becomes 0.
- Write a 0 below the dividend.
_________
11 | 8.00000000
0
Step 2: Multiply the remainder by 10, which is 8 x 10 = 80. Write this below the dividend, aligned with the previous remainder.
_________
11 | 8.00000000
0
- 0
80
Step 3: Divide 80 by 11.
- The quotient is 7.
- Write the quotient (7) above the division bar.
- Multiply the divisor (11) by the quotient (7), which gives us 77.
- Subtract 77 from 80, which gives us a remainder of 3.
_________
11 | 8.00000000
0
- 7
-----
30
Step 4: Bring down another 0 and divide 30 by 11.
- The quotient is 2.
- Write the quotient (2) above the division bar.
- Multiply the divisor (11) by the quotient (2), which gives us 22.
- Subtract 22 from 30, which gives us a remainder of 8.
_________
11 | 8.00000000
0
- 7
-----
30
- 22
-----
8
Step 5: At this point, we have a remainder of 8, which is the same as the original dividend 8. This indicates that the decimal expansion is repeating.
So, the fraction (8)/(11) as a repeating decimal is approximately 0.727272... with the cycle of repeating digits "72" marked by a bar above them.