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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 $\newline$ $\frac{2}{9}$ $\newline$ Edit the repeating and non-repeating part of the decimal: $\newline$ $0.\square\overline{\square}$

Full solution

Q. Convert the fraction below into a decimal

\newline

\frac{2}{9}

\newline

Edit the repeating and non-repeating part of the decimal:

\newline

0.\square\overline{\square}

Set Up Long Division: We start by setting up the long division of $2$ divided by $9$ . Since $2$ is less than $9$ , we add a decimal point to the quotient and add a zero to the dividend, making it $20$ .
Divide $20$ by $9$ : Now we divide $20$ by $9$ . $9$ goes into $20$ twice ( $2$ times $9$ is $18$ ), so we write $2$ in the quotient above the zero in the dividend.
Find Remainder: Subtract $18$ from $20$ to find the remainder. $20 - 18$ equals $2$ .
Add Another Zero: Since we have a remainder, we add another zero to the remainder and bring it down. Now we have $20$ again.
Repeat Division Process: We repeat the division process. Again, $9$ goes into $20$ twice, so we write another $2$ in the quotient after the decimal point.
Find Remainder Again: We subtract $18$ from $20$ again and find the remainder to be $2$ , just like before.
Conclude Decimal Form: This process will continue indefinitely because the remainder is repeating. We can conclude that the decimal form of $\frac{2}{9}$ is $0.222\ldots$ , with the digit $2$ repeating.
Edit Decimal Parts: Edit the repeating and non-repeating part of the decimal: The non-repeating part is $0$ , and the repeating part is \.222\ldots