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Convert the fraction below into a decimal

(2)/(9)
Edit the repeating and non-repeating part of the decimal:

0". "

Convert the fraction below into a decimal\newline29 \frac{2}{9} \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\newline29 \frac{2}{9} \newlineEdit the repeating and non-repeating part of the decimal:\newline0. 0.\square\overline{\square}
  1. Set Up Long Division: We start by setting up the long division of 22 divided by 99. Since 22 is less than 99, we add a decimal point to the quotient and add a zero to the dividend, making it 2020.
  2. Divide 2020 by 99: Now we divide 2020 by 99. 99 goes into 2020 twice (22 times 99 is 1818), so we write 22 in the quotient above the zero in the dividend.
  3. Find Remainder: Subtract 1818 from 2020 to find the remainder. 201820 - 18 equals 22.
  4. Add Another Zero: Since we have a remainder, we add another zero to the remainder and bring it down. Now we have 2020 again.
  5. Repeat Division Process: We repeat the division process. Again, 99 goes into 2020 twice, so we write another 22 in the quotient after the decimal point.
  6. Find Remainder Again: We subtract 1818 from 2020 again and find the remainder to be 22, just like before.
  7. Conclude Decimal Form: This process will continue indefinitely because the remainder is repeating. We can conclude that the decimal form of 29\frac{2}{9} is 0.2220.222\ldots, with the digit 22 repeating.
  8. Edit Decimal Parts: Edit the repeating and non-repeating part of the decimal: The non-repeating part is 00, and the repeating part is \.222\ldots

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