Express 7/13 as a repeating decimal. Mark the repeating digits with a bar
To express 7/13 as a repeating decimal, we first divide 7 by 13.
0.538461538461538....
The digit sequence 538461 repeats continuously, so we can write it as:
0.538461¯
Thus, 7/13 expressed as a repeating decimal is 0.538461¯.
To express 7/13 as a repeating decimal, we need to perform long division.
Starting with the division equation: 7 ÷ 13, we can write the division steps as follows:
0.5384... (dividend: 7, divisor: 13)
The first step is to divide 7 by 13:
- We find that 13 goes into 7 zero times, so we place a 0 above the division line.
Next, we bring down a 0 from the next digit of the dividend (if there is any) and divide 70 by 13 (the new dividend):
- 13 goes into 70 five times, so we place a 5 above the division line.
- We multiply 5 by 13, which equals 65, and subtract it from 70, leaving us with a remainder of 5.
Now, we bring down another 0 from the next digit of the dividend and divide 50 by 13 (the new dividend):
- 13 goes into 50 three times, so we place a 3 above the division line.
- We multiply 3 by 13, which equals 39, and subtract it from 50, leaving us with a remainder of 11.
Since we now have a remainder, we continue the division process by bringing down another 0 from the next digit of the dividend and divide 110 by 13 (the new dividend):
- 13 goes into 110 eight times, so we place an 8 above the division line.
- We multiply 8 by 13, which equals 104, and subtract it from 110, leaving us with a remainder of 6.
We continue bringing down 0s and performing the division until we either reach a remainder of 0 or the same remainder twice, which indicates that the decimal repeats. In this case, we notice that the remainder 6 repeats. So, we can mark the repeating digits with a bar.
Therefore, 7/13 expressed as a repeating decimal is 0.538461538461... (with the numbers 538461 repeating)
To express 7/13 as a repeating decimal with the repeating digits marked with a bar, follow these steps:
1. Divide the numerator (7) by the denominator (13) using long division.
```
0.5384615...
___________
13 | 7.000000000
- 6.5
-----
5.0
- 4.5
----
50
- 39
---
110
- 91
---
19
```
2. As you continue the long division, you'll notice that the digits start to repeat after the decimal point. In this case, the repeating digit sequence is 538461.
3. To mark the repeating digits with a bar, place a bar over the sequence obtained in the previous step. The final result is 0.5384615...
Therefore, 7/13 as a repeating decimal with the repeating digits marked with a bar is 0.5384615...