What is 7/13 expressed as a repeating decimal
The decimal representation of 7/13 as a repeating decimal is 0.538461538461...
To convert 7/13 to a repeating decimal, you can perform long division. Here's how:
Step 1: Place the dividend (7) inside the division bracket and the divisor (13) outside the division bracket.
__________
13 | 7
Step 2: Look at the quotient, which in this case is 0, and place it above the division bracket.
0
_________
13 | 7
Step 3: Multiply the divisor (13) by the quotient (0) and write the product below the dividend.
0
_________
13 | 7
0
Step 4: Subtract the product (0) from the dividend (7) to find the remainder.
0
_________
13 | 7
-0
_________
7
Step 5: Bring down the next digit of the dividend, which is a zero.
07
_________
13 | 7
Step 6: Divide the new dividend (70) by the divisor (13) again.
05
_________
13 | 70
Step 7: Multiply the divisor (13) by the new quotient (5) and write the product below the dividend.
05
_________
13 | 70
-65
_________
5
Step 8: Since the remainder is still not zero, bring down another zero.
057
_________
13 | 70
Step 9: Divide the new dividend (570) by the divisor (13) once more.
057
_________
13 | 570
- 520
_________
50
Step 10: Multiply the divisor (13) by the new quotient (4) and write the product below the dividend.
0574
_________
13 | 570
- 520
_________
50
Step 11: There is still a remainder of 50. To express this remainder as a repeating decimal, we can put a bar over the digits that will repeat. In this case, we just have one digit repeating, which is 3.
Therefore, 7/13 as a repeating decimal is approximately 0.538461538...