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

Question

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Answer 1

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

1. Divide 7 by 13. Since 7 is less than 13, we start by appending a decimal point and appending a zero, turning it into 70.
2. 13 goes into 70 five times (5 × 13 = 65).
3. Subtract 65 from 70, which gives you 5. Bring down another zero to make it 50.
4. 13 goes into 50 three times (3 × 13 = 39).
5. Subtract 39 from 50, which gives you 11. Bring down another zero to make it 110.
6. 13 goes into 110 eight times (8 × 13 = 104).
7. Subtract 104 from 110, which gives you 6. Bring down another zero to make it 60.
8. 13 goes into 60 four times (4 × 13 = 52).
9. Subtract 52 from 60, which gives you 8. Bring down another zero to make it 80.
10. 13 goes into 80 six times (6 × 13 = 78).
11. Subtract 78 from 80, which gives you 2. Bring down another zero to make it 20.
12. 13 goes into 20 once (1 × 13 = 13).
13. Subtract 13 from 20, which gives you 7. Bring down another zero to revert back to 70.

At this point, we see that we are back at the beginning of our long division.

Putting it all together, we find that: \[ \frac{7}{13} = 0.538461538461\ldots \]

The repeating part of the decimal is "538461".

Thus, we can write: \[ \frac{7}{13} = 0.\overline{538461} \]

So, the final answer is: \[ 0.\overline{538461} \]

Answer 2

i aint a robot.. make it simple

Answer 3

Sure! To express \( \frac{7}{13} \) as a repeating decimal, you can use long division.

When you divide 7 by 13, you get:

\[ \frac{7}{13} = 0.538461538461\ldots \]

The digits "538461" repeat.

So, we write it as:

\[ 0.\overline{538461} \]

That’s the repeating decimal for \( \frac{7}{13} \)!