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)

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. Since the remainder 1 keeps repeating, we get a repeating sequence of 3 in the decimal places. Therefore, the decimal equivalent of 10/3 is 3.3333..., 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. The correct representation of the repeating decimal 3.3333... is 3 with a bar over the 3. This matches with choice (D) 3. bar(3).

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Math Problems

Algebra 1

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) $3.\overline{3}$ .