Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard
To express 7/13 as a repeating decimal, you can divide 7 by 13 using long division. The quotient will be the non-repeating part of the decimal, and the remainder will be the repeating part.
0.538461538461538...
In this case, the digits 538461 repeat indefinitely. To represent this repeating part, you can place a bar over those digits:
0.538461̅
To express 7/13 as a repeating decimal, you can use long division to find the decimal representation.
```
0.538461538461538461538461538...
```
The digits 538461 repeat continuously. Therefore, the fraction 7/13 as a repeating decimal is 0.538461538461538461538461538... with the digits 538461 under a line.
To express 7/13 as a repeating decimal, we need to divide 7 by 13. Here's how you can do it:
Step 1: Start with the long division setup. Write 7 as the dividend inside the long division symbol (÷) and write 13 as the divisor outside the symbol.
0. | 7
------
Step 2: Perform the division. Divide 7 by 13. Since 7 is less than 13, we need to bring down a zero after the decimal point.
0. | 7
------
0.0
Step 3: Multiply the quotient (0) by the divisor (13) and subtract it from the previous result. Write the subtraction result below the line. Then, bring down the next digit of the dividend.
0. | 7
------
0.0
- 0
-----
70
Step 4: Repeat the process until you either find the repeating pattern or the division ends. In this case, 70 is still less than 13, so we need to bring down another zero after the previous result.
0. | 7
------
0.0
- 0
-----
70
0
Step 5: Multiply the new quotient (0) by the divisor (13) and subtract it from the previous result. Repeat the process until you find the repeating pattern or the division ends. In this case, 70 is still less than 13, so we bring down another zero.
0. | 7
------
0.0
- 0
-----
70
0 0
Step 6: Multiply the new quotient (0) by the divisor (13) and subtract it from the previous result. Repeat the process until you find the repeating pattern or the division ends. In this case, 70 is still less than 13, so we bring down another zero.
0. | 7
------
0.0
- 0
-----
70
0 0 0
Step 7: Multiply the new quotient (0) by the divisor (13) and subtract it from the previous result. Repeat the process until you find the repeating pattern or the division ends. In this case, the quotient is 0.538 (rounded to three decimal places).
0. | 7
------
0.0
- 0
-----
70
0 0 0 5
- 0
------
50
Step 8: At this point, we have a remainder of 5. Since we have encountered this remainder before in our division, we can conclude that the decimal portion of 7/13 repeats. Therefore, to express 7/13 as a repeating decimal, we can write it as 0.538 with the digits 538 repeating indefinitely. To indicate the repeating digits, we can place a bar over them. So, the final answer is:
7/13 = 0.538̅