How do you write 0.1{6} as a fraction? Choices: (A)1/6 (B)1/3 (C)1/8 (D)1/9

Recognize decimal pattern: Recognize the repeating decimal 0.1{6} as 0.16666... Assign variable and multiply: Let x = 0.16666... Multiply x by 10 to shift the decimal point: 10x = 1.6666... Subtract to eliminate repetition: Subtract the original x from 10x to eliminate the repeating part: 10x - x = 1.6666... - 0.16666... Simplify the equation: Simplify the subtraction: 9x = 1.5

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How do you write $0.1\overline{6}$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{6}$ $\newline$ (B) $\frac{1}{3}$ $\newline$ (C) $\frac{1}{8}$ $\newline$ (D) $\frac{1}{9}$

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Math Problems

Grade 8

Convert between repeating decimals and fractions

Full solution

Q. How do you write

0.1\overline{6}

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{6}

\newline

(B)

\frac{1}{3}

\newline

(C)

\frac{1}{8}

\newline

(D)

\frac{1}{9}

Recognize decimal pattern: Recognize the repeating decimal $0.1\overline{6}$ as $0.16666\ldots$
Assign variable and multiply: Let $x = 0.16666\ldots$ Multiply $x$ by $10$ to shift the decimal point: $10x = 1.6666\ldots$
Subtract to eliminate repetition: Subtract the original $x$ from $10x$ to eliminate the repeating part: $10x - x = 1.6666... - 0.16666...$
Simplify the equation: Simplify the subtraction: $9x = 1.5$