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Convert the fraction below into a decimal

(7)/(12)
Edit the repeating and non-repeating part of the decimal:

0". "

Convert the fraction below into a decimal\newline712 \frac{7}{12} \newlineEdit the repeating and non-repeating part of the decimal:\newline0. 0.\square\overline{\square}

Full solution

Q. Convert the fraction below into a decimal\newline712 \frac{7}{12} \newlineEdit the repeating and non-repeating part of the decimal:\newline0. 0.\square\overline{\square}
  1. Understand division process: Understand the division process for converting a fraction to a decimal.\newlineTo convert the fraction 712\frac{7}{12} into a decimal, we need to perform the division of the numerator by the denominator.
  2. Set up division of 77 by 1212: Set up the division of 77 by 1212. We write 77 as 7.0007.000, adding three decimal places for the division, and divide it by 1212.
  3. Perform division: Perform the division.\newline1212 goes into 7070 five times (5×12=605 \times 12 = 60), so we write 55 above the line after the decimal point. Subtract 6060 from 7070 to get a remainder of 1010. Bring down the next 00 to make it 100100.
  4. Continue division: Continue the division.\newline1212 goes into 100100 eight times (8×12=968 \times 12 = 96), so we write 88 next to the 55 in the quotient. Subtract 9696 from 100100 to get a remainder of 44. Bring down the next 00 to make it 4040.
  5. Finish division: Finish the division. 1212 goes into 4040 three times (3×12=363 \times 12 = 36), so we write 33 next to the 88 in the quotient. Subtract 3636 from 4040 to get a remainder of 44. Since the remainder is repeating the previous remainder, we can stop the division here as the decimal will start to repeat.
  6. Write final answer: Write the final answer.\newlineThe division gives us the decimal 0.5830.583, and since the remainder has started to repeat, we know that the decimal does not continue further.

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