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Which decimal is equivalent to
(10)/(3) ?
Choose 1 answer:
(A)
0. bar(3)
(B)
1. bar(3)
(c)
3. bar(1)
(D)
3. bar(3)

Which decimal is equivalent to $\frac{10}{3}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $0 . \overline{3}$ $\newline$ (B) $1 . \overline{3}$ $\newline$ (C) $3 . \overline{1}$ $\newline$ (D) $3 . \overline{3}$

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Identify equivalent linear expressions

Full solution

Q. Which decimal is equivalent to

\frac{10}{3}

?

\newline

Choose

1

answer:

\newline

(A)

0 . \overline{3}

\newline

(B)

1 . \overline{3}

\newline

(C)

3 . \overline{1}

\newline

(D)

3 . \overline{3}

Understand Division Process: Understand the division of $10$ by $3$ . When we divide $10$ by $3$ , we are trying to find out how many times $3$ goes into $10$ and what the remainder is.
Perform Division: Perform the division. $10$ divided by $3$ gives us $3$ with a remainder of $1$ . However, when we continue the division to get a decimal, the remainder of $1$ will keep repeating because $10$ is not a multiple of $3$ .
Determine Repeating Decimal: Determine the repeating decimal. $\newline$ Since the remainder $1$ keeps repeating, we get a repeating sequence of $3$ in the decimal places. Therefore, the decimal equivalent of $\frac{10}{3}$ is $3.3333\ldots$ , which is represented as $3$ with a bar over the $3$ to indicate that it repeats indefinitely.
Match with Choices: Match the result with the given choices. $\newline$ The correct representation of the repeating decimal $3.3333\ldots$ is $3$ with a bar over the $3$ . This matches with choice (D) $3.\overline{3}$ .

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