Which fractions are equivalent to 0.1{7}? Select all that apply. Multi-select Choices: (A)177/1,000 (B)16/90 (C)8/45 (D)17/100

Convert to fraction: Convert 0.1(7) to a fraction by recognizing it as 0.17 repeating. Let x = 0.171717... Multiply x by 100 to shift the decimal point: 100x = 17.171717... Subtract the original x from this equation: 100x - x = 17.171717... - 0.171717... This simplifies to 99x = 17. Solve for x: Solve for x by dividing both sides by 99: x = 17 / 99. This fraction represents the decimal 0.1(7). Check options: Check each option to see if it simplifies to 17/99: (A) 177/1,000 does not simplify to 17/99. (B) 16/90 simplifies to 8/45, which needs further checking. (C) 8/45 simplifies to 8/45, which is the same as 16/90. (D) 17/100 does not simplify to 17/99. Simplify 8/45: Simplify 8/45 to check if it equals 17/99. Divide both numerator and denominator by their GCD, which is 1, so 8/45 remains 8/45. This does not equal 17/99.

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Which fractions are equivalent to $0.1\overline{7}$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $\frac{177}{1,000}$ $\newline$ (B) $\frac{16}{90}$ $\newline$ (C) $\frac{8}{45}$ $\newline$ (D) $\frac{17}{100}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Which fractions are equivalent to

0.1\overline{7}

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

\frac{177}{1,000}

\newline

(B)

\frac{16}{90}

\newline

(C)

\frac{8}{45}

\newline

(D)

\frac{17}{100}

Convert to fraction: Convert $0.1(7)$ to a fraction by recognizing it as $0.17$ repeating. Let $x = 0.171717\ldots$ Multiply $x$ by $100$ to shift the decimal point: $100x = 17.171717\ldots$ Subtract the original $x$ from this equation: $100x - x = 17.171717\ldots - 0.171717\ldots$ This simplifies to $99x = 17$ .
Solve for x: Solve for x by dividing both sides by $99$ : $x = \frac{17}{99}$ . This fraction represents the decimal $0.1(7)$ .
Check options: Check each option to see if it simplifies to $\frac{17}{99}$ : $\newline$ (A) $\frac{177}{1,000}$ does not simplify to $\frac{17}{99}$ . $\newline$ (B) $\frac{16}{90}$ simplifies to $\frac{8}{45}$ , which needs further checking. $\newline$ (C) $\frac{8}{45}$ simplifies to $\frac{8}{45}$ , which is the same as $\frac{16}{90}$ . $\newline$ (D) $\frac{17}{100}$ does not simplify to $\frac{17}{99}$ .
Simplify $\frac{8}{45}$ : Simplify $\frac{8}{45}$ to check if it equals $\frac{17}{99}$ . Divide both numerator and denominator by their GCD, which is $1$ , so $\frac{8}{45}$ remains $\frac{8}{45}$ . This does not equal $\frac{17}{99}$ .