How do you write 0.166666 as a fraction? Choices: (A)1/8 (B)1/5 (C)1/3 (D)1/6

Recognize as repeating decimal: Convert the decimal 0.166666 to a fraction by recognizing it as a repeating decimal. Write it as 0.166666... Multiply by 10^6: Since the decimal repeats every 6, multiply 0.166666... by 10^6 (1000000) to shift the decimal point six places to the right, resulting in 166666.666... Set up equation: Set up the equation: 1000000x = 166666.666... where x = 0.166666... Subtract original x: Subtract the original x from the multiplied equation: 1000000x - x = 166666.666... - 0.166666... Simplify equation: Simplify the equation: 999999x = 166666.5

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How do you write $0.166666$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{8}$ $\newline$ (B) $\frac{1}{5}$ $\newline$ (C) $\frac{1}{3}$ $\newline$ (D) $\frac{1}{6}$

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Math Problems

Algebra 1

Convert between decimals and fractions

Full solution

Q. How do you write

0.166666

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{8}

\newline

(B)

\frac{1}{5}

\newline

(C)

\frac{1}{3}

\newline

(D)

\frac{1}{6}

Recognize as repeating decimal: Convert the decimal $0.166666$ to a fraction by recognizing it as a repeating decimal. Write it as $0.166666\ldots$
Multiply by $10^6$ : Since the decimal repeats every $6$ , multiply $0.166666...$ by $10^6$ ( $1000000$ ) to shift the decimal point six places to the right, resulting in $166666.666...$
Set up equation: Set up the equation: $1000000x = 166666.666\ldots$ where $x = 0.166666\ldots$
Subtract original x: Subtract the original x from the multiplied equation: $1000000x - x = 166666.666... - 0.166666...$
Simplify equation: Simplify the equation: $999999x = 166666.5$