Rational Numbers in Different Forms Practice
Math 8 Q1 (Pre-Algebra) / The Number System
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.
(1 point)
To express 7/13 as a repeating decimal, we divide 7 by 13:
7 ÷ 13 = 0.538461538...
The repeating digit is 538461, so we can write 7/13 as 0.538461 with a bar on top of the repeating part.
To express 7/13 as a repeating decimal, we can use long division. Here are the steps:
1. Set up the long division with 7 as the dividend and 13 as the divisor:
______
13 | 7
2. Divide 7 by 13. The quotient is 0, so we write 0 above the line as the first digit of the quotient:
0
______
13 | 7
3. Multiply the divisor (13) by 0, and subtract it from the dividend (7):
0
______
13 | 7
- 0
The difference is 7.
4. Bring down the next digit of the dividend, which is 0:
0
______
13 | 7 0
5. Divide 70 (the new dividend) by 13. The quotient is 5, so we write 5 above the line as the next digit of the quotient:
05
______
13 | 70
6. Multiply the divisor (13) by 5, and subtract it from the dividend (70):
05
______
13 | 70
- 65
The difference is 5.
7. Bring down the next digit of the dividend, which is 0:
05
______
13 | 70 0
8. Repeat steps 5-7 until you either reach a remainder of 0 or a repeating pattern emerges.
70 ÷ 13 = 5 with a remainder of 5.
50 ÷ 13 = 3 with a remainder of 11.
110 ÷ 13 = 8 with a remainder of 6.
60 ÷ 13 = 4 with a remainder of 8.
80 ÷ 13 = 6 with a remainder of 2.
20 ÷ 13 = 1 with a remainder of 7.
70 ÷ 13 = 5 with a remainder of 5.
...
At this point, a repeating pattern emerges with a remainder of 5. So the decimal representation of 7/13 is:
0.538461538461...
To indicate the repeating pattern, we can use a bar above the digits 538461:
0.538461̅
Therefore, 7/13 can be expressed as the repeating decimal 0.538461̅.