Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
To express 7/13 as a repeating decimal, we can perform long division.
The dividend is 7 and the divisor is 13. When we divide 7 by 13, we get a quotient of 0.
Next, we multiply 0 by 13 and subtract the result from 7:
7 - (0 * 13) = 7.
Now, we bring down a zero to the right of 7.
We continue the process by dividing 70 by 13. The quotient is 5.
Next, we multiply 5 by 13 and subtract the result from 70:
70 - (5 * 13) = 5.
Again, we bring down a zero to the right of 5.
We continue the process by dividing 50 by 13. The quotient is 3.
Next, we multiply 3 by 13 and subtract the result from 50:
50 - (3 * 13) = 11.
Again, we bring down a zero to the right of 11.
We continue the process by dividing 110 by 13. The quotient is 8.
Next, we multiply 8 by 13 and subtract the result from 110:
110 - (8 * 13) = 6.
Again, we bring down a zero to the right of 6.
Finally, we divide 60 by 13. The quotient is 4.
Next, we multiply 4 by 13 and subtract the result from 60:
60 - (4 * 13) = 8.
Since we keep getting the remainder 8 repeatedly, we can conclude that the decimal representation of 7/13 is a repeating decimal. Thus, 7/13 as a repeating decimal is 0.538(bar), where the digits 538 repeat indefinitely.
Express 7/13 as a repeating decimal
To express 7/13 as a repeating decimal, we can perform long division:
0.538461538461538461538...
-13 | 7.000000000000000000000...
-0
______
70
- 65
______
50
- 39
______
110
- 91
______
190
- 182
______
80
- 78
______
20
- 13
______
70
- 65
______
50
- 39
______
110
- 91
______
190
- 182
______
80
- 78
______
20
- 13
______
70
- 65
______
50
- 39
______
110
- 91
______
190
- 182
______
80
- 78
______
20
- 13
______
70
- 65
______
50
- 39
______
110
- 91
______
190
- 182
______
80
- 78
______
20
- 13
______
70
- 65
______
50...
As we can see, the sequence 538461 repeats indefinitely. Therefore, 7/13 as a repeating decimal is 0.538461538461538461538...
0.538461
To express 7/13 as a repeating decimal, we can use long division.
1. Begin by dividing 7 by 13:
0.538461538...
2. Notice that after the decimal point, the digits start repeating. To indicate this, we can place a bar over the repeating digits. Therefore, 7/13 is equal to 0.538461538...
To express a fraction as a repeating decimal, you need to divide the numerator (7) by the denominator (13) and look for a repeating pattern.
To do this, follow these steps:
1. Start by dividing 7 by 13:
7 ÷ 13 = 0.5384615384615...
2. Continue dividing until you notice a repeating pattern. In this case, you can see that the digits 538461 repeat.
3. To indicate the repeating pattern, place a bar above the repeating digits:
0.5384615384615... = 0. 538 461̅
So, the fraction 7/13 can be expressed as a repeating decimal as 0.538461̅, where the digits 538461 repeat.