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Express 7 / 13

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 ( ∠
∠
) keyboar

1 answer

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

  1. Divide \( 7.000000 \) by \( 13 \).
  2. \( 13 \) goes into \( 70 \) five times. \( 5 \times 13 = 65 \).
    • Subtract \( 65 \) from \( 70 \) to get \( 5 \).
  3. Bring down the next \( 0 \) to get \( 50 \).
  4. \( 13 \) goes into \( 50 \) three times. \( 3 \times 13 = 39 \).
    • Subtract \( 39 \) from \( 50 \) to get \( 11 \).
  5. Bring down another \( 0 \) to get \( 110 \).
  6. \( 13 \) goes into \( 110 \) eight times. \( 8 \times 13 = 104 \).
    • Subtract \( 104 \) from \( 110 \) to get \( 6 \).
  7. Bring down another \( 0 \) to get \( 60 \).
  8. \( 13 \) goes into \( 60 \) four times. \( 4 \times 13 = 52 \).
    • Subtract \( 52 \) from \( 60 \) to get \( 8 \).
  9. Bring down another \( 0 \) to get \( 80 \).
  10. \( 13 \) goes into \( 80 \) six times. \( 6 \times 13 = 78 \).
    • Subtract \( 78 \) from \( 80 \) to get \( 2 \).
  11. Bring down another \( 0 \) to get \( 20 \).
  12. \( 13 \) goes into \( 20 \) once. \( 1 \times 13 = 13 \).
    • Subtract \( 13 \) from \( 20 \) to get \( 7 \).

At this point, we are back where we started with \( 7 \), indicating that the digits \( 538461 \) will continue repeating.

Thus, we can express \( \frac{7}{13} \) as: \[ 0.\overline{538461} \] This indicates that the digits \( 538461 \) repeat indefinitely.