Express 7 over 13 as a repeating decimal. Mark the repeating digits with a bar.

Question

Note: You will find the option to add a bar above text in the Geometry ( ∠) keyboard.

Answer 1

To convert the fraction \( \frac{7}{13} \) into a decimal, we can perform long division.

1. Divide 7 by 13.
2. Since 7 is less than 13, we start with 0.
3. We add a decimal point and a zero: 70 divided by 13.
4. 13 goes into 70 a total of 5 times (since \( 13 \times 5 = 65 \)).
5. Subtract 65 from 70, which gives us 5. Bring down another 0 to make it 50.
6. 13 goes into 50 a total of 3 times (since \( 13 \times 3 = 39 \)).
7. Subtract 39 from 50, which gives us 11. Bring down another 0 to make it 110.
8. 13 goes into 110 a total of 8 times (since \( 13 \times 8 = 104 \)).
9. Subtract 104 from 110, which gives us 6. Bring down another 0 to make it 60.
10. 13 goes into 60 a total of 4 times (since \( 13 \times 4 = 52 \)).
11. Subtract 52 from 60, which gives us 8. Bring down another 0 to make it 80.
12. 13 goes into 80 a total of 6 times (since \( 13 \times 6 = 78 \)).
13. Subtract 78 from 80, which gives us 2. Bring down another 0 to make it 20.
14. 13 goes into 20 a total of 1 time (since \( 13 \times 1 = 13 \)).
15. Subtract 13 from 20, which gives us 7. Bring down another 0 to make it 70.

Now we can see that the process will repeat from step 4.

Thus, the repeating decimal for \( \frac{7}{13} \) is:

\[ 0.\overline{538461} \]

So, \( \frac{7}{13} \) as a repeating decimal is \( 0.\overline{538461} \).