Express 7 13 as repeating decimal mark the repeating with a bar
The fraction 7/13 can be expressed as a repeating decimal by long division or using a calculator.
Using long division, we start dividing 7 by 13:
```
0.
13) 7.00000000
- 0
7
```
Take the remainder (7) and add a decimal point after the zero in the quotient. Bring down another zero and divide:
```
0.5
13) 7.00000000
- 0
7
- 6
10
```
Now, bring down another zero and divide:
```
0.53
13) 7.00000000
- 0
7
- 6
10
- 9
10
```
Continue this process indefinitely to find the repeating decimal:
```
0.538461538461...
```
To indicate the repeating part, we place a bar over the digits that repeat:
0.538461538461...
Therefore, the decimal representation of 7/13 is 0.538461538461...
To express 7/13 as a repeating decimal with a bar, you can divide the numerator (7) by the denominator (13) using long division. Here are the steps:
1. Divide 7 by 13: 7 ÷ 13 = 0 with a remainder of 7. Write down the quotient (0) above the division symbol.
0.
-------
13 | 7
2. Multiply the remainder (7) by 10 to bring down the next digit: 7 × 10 = 70. Write down 70 below the division line.
0.
-------
13 | 7
- -
70
3. Divide 70 by 13: 70 ÷ 13 = 5 with a remainder of 5. Write down the quotient (5) next to the 0.
0.5
-------
13 | 7
- 5
70
4. Multiply the remainder (5) by 10 to bring down the next digit: 5 × 10 = 50. Write down 50 below the division line.
0.53
-------
13 | 7
- 5
70
- 65
5. Divide 50 by 13: 50 ÷ 13 = 3 with a remainder of 11. Write down the quotient (3) next to the 5.
0.538
-------
13 | 7
- 5
70
- 65
- 39
6. Multiply the remainder (11) by 10 to bring down the next digit: 11 × 10 = 110. Write down 110 below the division line.
0.5384
-------
13 | 7
- 5
70
- 65
- 39
- 39
7. Divide 110 by 13: 110 ÷ 13 = 8 with a remainder of 6. Write down the quotient (8) next to the 3.
0.538461
-------
13 | 7
- 5
70
- 65
- 39
- 39
6
The pattern of the remainders repeats from this point onward. So, the repeating decimal form of 7/13 is 0.538461538461... (with the digits 538461 repeating).