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Which decimal is equivalent to
(25)/(6) ?
Choose 1 answer:
(A)
4. bar(1)
(B)
4. bar(16)
(C)
4.1 bar(6)
(D)
4.1 bar(667)

Which decimal is equivalent to $\frac{25}{6}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $4 . \overline{1}$ $\newline$ (B) $4 . \overline{16}$ $\newline$ (C) $4.1 \overline{6}$ $\newline$ (D) $4.1 \overline{667}$

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Identify equivalent linear expressions

Full solution

Q. Which decimal is equivalent to

\frac{25}{6}

?

\newline

Choose

1

answer:

\newline

(A)

4 . \overline{1}

\newline

(B)

4 . \overline{16}

\newline

(C)

4.1 \overline{6}

\newline

(D)

4.1 \overline{667}

Divide and Convert: Divide $25$ by $6$ to convert the fraction into a decimal. $\newline$ $25 \div 6 = 4$ with a remainder of $1$ .
Continue Division: Since there is a remainder, we continue the division to find the decimal representation. We add a decimal point to the quotient and bring down a zero to the remainder to continue the division. $\newline$ $10 \div 6 = 1$ with a remainder of $4$ .
Decimal Representation: We bring down another zero to the remainder and continue the division. $\newline$ $40 \div 6 = 6$ with a remainder of $4$ .
Identify Repeating Pattern: Notice that we are getting a remainder of $4$ again, which indicates that the division will repeat the same pattern, resulting in a repeating decimal.
Final Decimal Expansion: Since the remainder repeats after every division by $6$ , the decimal expansion of $\frac{25}{6}$ is $4.1\overline{6}$ with the $6$ repeating.

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