How do you write 0.08{3} as a fraction? Choices: (A)1/12 (B)1/4 (C)1/6 (D)1/8

Identify Repeating Decimal: Step 1: Identify the repeating decimal. 0.08{3} means 0.0833333... where 3 is repeating. Shift Decimal Point: Step 2: Let x = 0.0833333... Multiply x by 1000 to shift the decimal point: 1000x = 833.3333... Multiply by 10: Step 3: Also, multiply x by 10: 10x = 0.833333... Subtract Equations: Step 4: Subtract the equation in Step 3 from the equation in Step 2 to eliminate the repeating part. 1000x - 10x = 833.3333... - 0.833333... This gives 990x = 832.5

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How do you write $0.08\overline{3}$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{12}$ $\newline$ (B) $\frac{1}{4}$ $\newline$ (C) $\frac{1}{6}$ $\newline$ (D) $\frac{1}{8}$

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Math Problems

Grade 8

Convert between repeating decimals and fractions

Full solution

Q. How do you write

0.08\overline{3}

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{12}

\newline

(B)

\frac{1}{4}

\newline

(C)

\frac{1}{6}

\newline

(D)

\frac{1}{8}

Identify Repeating Decimal: Step $1$ : Identify the repeating decimal. $0.08\{3\}$ means $0.0833333\ldots$ where $3$ is repeating.
Shift Decimal Point: Step $2$ : Let $x = 0.0833333\ldots$ Multiply $x$ by $1000$ to shift the decimal point: $1000x = 833.3333\ldots$
Multiply by $10$ : Step $3$ : Also, multiply $x$ by $10$ : $10x = 0.833333\ldots$
Subtract Equations: Step $4$ : Subtract the equation in Step $3$ from the equation in Step $2$ to eliminate the repeating part. $1000x - 10x = 833.3333... - 0.833333...$ This gives $990x = 832.5$