Which decimal is equivalent to $\frac{26}{9}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2$ . $8$ $\newline$ (B) $2 . \overline{8}$ $\newline$ (C) $\mathbf{2 . 8 8 9}$ $\newline$ (D) $2$ . $9$

Full solution

Q. Which decimal is equivalent to

\frac{26}{9}

\newline

Choose

1

answer:

\newline

(A)

2

8

\newline

(B)

2 . \overline{8}

\newline

(C)

\mathbf{2 . 8 8 9}

\newline

(D)

2

9

Divide and Convert: Divide $26$ by $9$ to convert the fraction into a decimal. $\newline$ $26 \div 9 = 2$ remainder $8$ $\newline$ $2$ is the whole number part, and we have a remainder of $8$ .
Find Decimal Part: To find the decimal part, we continue the division by considering the remainder. Since $8$ is less than $9$ , we add a decimal point to $2$ (the quotient) and add a zero to the remainder to continue the division. $\newline$ $8$ becomes $80$ when we add a zero. $\newline$ $80 \div 9 = 8$ with a remainder of $8$ . $\newline$ The quotient is $2.8$ with another $8$ repeating.
Recognize Repeating Pattern: Recognize that the remainder is repeating. Since we have a remainder of $8$ again, this process will continue indefinitely, giving us a repeating decimal. $\newline$ The decimal equivalent of $(26)/(9)$ is $2.8$ with the $8$ repeating.
Choose Correct Answer: Choose the correct answer from the given options that matches the repeating decimal. $\newline$ The correct answer is (B) $2.\overline{8}$ , which represents the repeating decimal $2.888\ldots$