Which decimal is equivalent to $\frac{29}{11}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2.6 \overline{3}$ $\newline$ (B) $2$ . $6363$ $\newline$ (C) $2 . \overline{63}$ $\newline$ (D) $2 . \overline{6}$

Full solution

Q. Which decimal is equivalent to

\frac{29}{11}

\newline

Choose

1

answer:

\newline

(A)

2.6 \overline{3}

\newline

(B)

2

6363

\newline

(C)

2 . \overline{63}

\newline

(D)

2 . \overline{6}

Divide and Find Decimal: Divide $29$ by $11$ to find the decimal equivalent. $\newline$ Calculation: $29 \div 11 = 2$ with a remainder of $7$ .
Continue Division with Remainder: Since there is a remainder, we continue the division to find the decimal part. $\newline$ Calculation: We add a decimal point to $2$ (the quotient) and bring down a zero to the remainder to continue the division. Now we have $70$ to divide by $11$ .
Divide $70$ by $11$ : Divide $70$ by $11$ . $\newline$ Calculation: $70 \div 11 = 6$ with a remainder of $4$ .
Continue Division Process: Since there is still a remainder, we continue the division process. $\newline$ Calculation: We bring down another zero to the remainder to continue the division. Now we have $40$ to divide by $11$ .
Divide $40$ by $11$ : Divide $40$ by $11$ . $\newline$ Calculation: $40 \div 11 = 3$ with a remainder of $7$ .
Identify Repeating Remainders: Notice the pattern of remainders. We have a repeating remainder of $7$ , which means the division will cycle through the same sequence of numbers. $\newline$ Calculation: The decimal part of the quotient will repeat the sequence ＂ $63$ ＂ indefinitely.
Write Decimal Equivalent: Write the decimal equivalent with the repeating sequence. $\newline$ Calculation: The decimal equivalent of $\frac{29}{11}$ is $2.\overline{63}$ with the $\overline{63}$ part repeating.