Express 713

Question

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.

Answer 1

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

1. Divide 7 by 13. Initially, 7 is less than 13, so we add a decimal point and a zero, treating it as 70.
2. 13 goes into 70 five times (since \( 13 \times 5 = 65 \)).
3. Subtract 65 from 70, which gives us 5. Bring down another 0 to make it 50.
4. 13 goes into 50 three times (since \( 13 \times 3 = 39 \)).
5. Subtract 39 from 50, which gives us 11. Bring down another 0 to get 110.
6. 13 goes into 110 eight times (since \( 13 \times 8 = 104 \)).
7. Subtract 104 from 110, which gives us 6. Bring down another 0 to make it 60.
8. 13 goes into 60 four times (since \( 13 \times 4 = 52 \)).
9. Subtract 52 from 60, which gives us 8. Bring down another 0 to get 80.
10. 13 goes into 80 six times (since \( 13 \times 6 = 78 \)).
11. Subtract 78 from 80, which gives us 2. Bring down another 0 to make it 20.
12. 13 goes into 20 once (since \( 13 \times 1 = 13 \)).
13. Subtract 13 from 20, which gives us 7. Bring down another 0, and we’re back to where we started.

At this point, we can see that the digits will start repeating after 6: 538461.

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

\[ 0.\overline{538461} \]

This notation indicates that "538461" repeats indefinitely.