Express

Question

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)

Answer 1

To express \( \frac{7}{13} \) as a repeating decimal, we can perform long division.

When we divide 7 by 13, we can calculate it as follows:

1. 7.000000 divided by 13
2. 13 goes into 70 five times (5 * 13 = 65).
3. Subtract 65 from 70, we get 5.
4. Bring down a 0, making it 50.
5. 13 goes into 50 three times (3 * 13 = 39).
6. Subtract 39 from 50, we get 11.
7. Bring down a 0, making it 110.
8. 13 goes into 110 eight times (8 * 13 = 104).
9. Subtract 104 from 110, we get 6.
10. Bring down a 0, making it 60.
11. 13 goes into 60 four times (4 * 13 = 52).
12. Subtract 52 from 60, we get 8.
13. Bring down a 0, making it 80.
14. 13 goes into 80 six times (6 * 13 = 78).
15. Subtract 78 from 80, we get 2.
16. Bring down a 0, making it 20.
17. 13 goes into 20 one time (1 * 13 = 13).
18. Subtract 13 from 20, we get 7, which brings us back to where we started, with 7.

The repeating decimal starts at this point since we are back to the number 7.

Thus, \( \frac{7}{13} \) as a repeating decimal is:

\[ 0.\overline{538461} \]

So, the final answer is:

\[ 0.\overline{538461} \]

Answer 2

Convert 0.8 to a rational number. (1 point)