How do you write 0.{3} as a fraction? Choices: (A)1/3 (B)1/9 (C)1/6 (D)1/4

Identify Repeating Decimal: Identify the repeating decimal. 0.{3} means 0.3333... which is a repeating decimal. Assign Variable and Shift Decimal: Let x = 0.3333... Multiply both sides by 10 to shift the decimal point. 10x = 3.3333... Subtract to Eliminate Repeating Part: Subtract the original x from 10x to eliminate the repeating part. 10x - x = 3.3333... - 0.3333... This gives 9x = 3. Solve for x: Solve for x by dividing both sides by 9. x = 3 / 9. Simplify the fraction to x = 1/3.

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How do you write $0.\overline{3}$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{3}$ $\newline$ (B) $\frac{1}{9}$ $\newline$ (C) $\frac{1}{6}$ $\newline$ (D) $\frac{1}{4}$

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Math Problems

Grade 6

Convert between fractions and repeating decimals

Full solution

Q. How do you write

0.\overline{3}

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{3}

\newline

(B)

\frac{1}{9}

\newline

(C)

\frac{1}{6}

\newline

(D)

\frac{1}{4}

Identify Repeating Decimal: Identify the repeating decimal. $0.\overline{3}$ means $0.3333\ldots$ which is a repeating decimal.
Assign Variable and Shift Decimal: Let $x = 0.3333\ldots$ Multiply both sides by $10$ to shift the decimal point. $10x = 3.3333\ldots$
Subtract to Eliminate Repeating Part: Subtract the original $x$ from $10x$ to eliminate the repeating part. $10x - x = 3.3333... - 0.3333...$ This gives $9x = 3$ .
Solve for x: Solve for x by dividing both sides by $9$ . $x = \frac{3}{9}$ . Simplify the fraction to $x = \frac{1}{3}$ .