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 express \( \frac{7}{13} \) as a repeating decimal, we can perform the division of 7 by 13.

1. Dividing 7 by 13 gives us:

   • 0 (since 7 is less than 13)
   • We can add a decimal point and then 0s to the dividend (making it 70).

2. Now, 13 goes into 70 five times (since \( 5 \times 13 = 65 \)):

   • So we write down 0.5 and subtract 65 from 70, getting 5.

3. Bring down the next 0 to get 50:

   • 13 goes into 50 three times (since \( 3 \times 13 = 39 \)):
   • Write down 3 and subtract 39 from 50, getting 11.

4. Bring down the next 0 to get 110:

   • 13 goes into 110 eight times (since \( 8 \times 13 = 104 \)):
   • Write down 8 and subtract 104 from 110, getting 6.

5. Bring down the next 0 to get 60:

   • 13 goes into 60 four times (since \( 4 \times 13 = 52 \)):
   • Write down 4 and subtract 52 from 60, getting 8.

6. Bring down the next 0 to get 80:

   • 13 goes into 80 six times (since \( 6 \times 13 = 78 \)):
   • Write down 6 and subtract 78 from 80, getting 2.

7. Bring down the next 0 to get 20:

   • 13 goes into 20 one time (since \( 1 \times 13 = 13 \)):
   • Write down 1 and subtract 13 from 20, getting 7.

Now we have come back to our original remainder of 7, and the cycle will start again.

So, the decimal representation of \( \frac{7}{13} \) is \( 0.538461538461... \)

Thus, we can express it as:

\[ 0.\overline{538461} \]

The repeating part is \( 538461 \).