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

Answer 1

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

1. Divide 7 by 13. Since 7 is less than 13, we start with 0. We can write \( 7.000000 \) to facilitate the division.
2. 13 goes into 70 five times (since \( 13 \times 5 = 65 \)).
3. Subtract 65 from 70, which gives us 5.
4. Bring down the next 0, making it 50. 13 goes into 50 three times (since \( 13 \times 3 = 39 \)).
5. Subtract 39 from 50, which gives us 11.
6. Bring down the next 0, making it 110. 13 goes into 110 eight times (since \( 13 \times 8 = 104 \)).
7. Subtract 104 from 110, which gives us 6.
8. Bring down the next 0, making it 60. 13 goes into 60 four times (since \( 13 \times 4 = 52 \)).
9. Subtract 52 from 60, which gives us 8.
10. Bring down the next 0, making it 80. 13 goes into 80 six times (since \( 13 \times 6 = 78 \)).
11. Subtract 78 from 80, which gives us 2.
12. Bring down the next 0, making it 20. 13 goes into 20 once (since \( 13 \times 1 = 13 \)).
13. Subtract 13 from 20, which gives us 7.

At this point, we see that we are back to dividing 7 by 13, indicating that the decimal will repeat.

So, the repeating decimal for \( \frac{7}{13} \) is \( 0.538461538461\ldots \).

Thus, we can express it as:

\[ 0.\overline{538461} \]

Where the bar indicates that "538461" is the repeating part.