How do you write 0.111111 as a fraction? Choices: (A)1/6 (B)1/3 (C)1/10 (D)1/9

Set Decimal as x: Convert the repeating decimal to a fraction by setting it as x: x = 0.111111... Recognize Repeating Part: Recognize the repeating part (1) and set up an equation by shifting the decimal point: 10x = 1.111111... Set Up Equation: Subtract the original x from the 10x equation to eliminate the repeating decimals: 10x - x = 1.111111... - 0.111111... Simplify Equation: Simplify the equation: 9x = 1; then solve for x by dividing both sides by 9: x = 1/9

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How do you write $0.111111$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{6}$ $\newline$ (B) $\frac{1}{3}$ $\newline$ (C) $\frac{1}{10}$ $\newline$ (D) $\frac{1}{9}$

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Math Problems

Algebra 1

Convert between decimals and fractions

Full solution

Q. How do you write

0.111111

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{6}

\newline

(B)

\frac{1}{3}

\newline

(C)

\frac{1}{10}

\newline

(D)

\frac{1}{9}

Set Decimal as $x$ : Convert the repeating decimal to a fraction by setting it as $x$ : $x = 0.111111...$
Recognize Repeating Part: Recognize the repeating part $1$ and set up an equation by shifting the decimal point: $10x = 1.111111\ldots$
Set Up Equation: Subtract the original $x$ from the $10x$ equation to eliminate the repeating decimals: $10x - x = 1.111111... - 0.111111...$
Simplify Equation: Simplify the equation: $9x = 1$ ; then solve for $x$ by dividing both sides by $9$ : $x = \frac{1}{9}$