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

Convert to fraction: Convert 0.1(7) to a fraction. Since 0.1(7) means 0.177777..., let x = 0.177777... Multiplying by 100, we get 100x = 17.7777... Subtracting the original x from this, 100x - x = 17.7777... - 0.177777... results in 99x = 17.6. Solving for x gives x = 17.6 / 99. Simplify fraction: Simplify the fraction 17.6/99. Since 17.6 can be written as 176/10, the fraction becomes 176/990. Simplifying by dividing numerator and denominator by 2, we get 88/495. Check option (A): Check each option to see if it simplifies to 88/495. For (A) 16/90, simplifying by dividing numerator and denominator by 2 gives 8/45. Check option (B): For (B) 17/100, this fraction is already in its simplest form and does not equal 88/495. Check option (C): For (C) 8/45, this was obtained from simplifying 16/90, which we already found to be equivalent to 88/495. Check option (D): For (D) 177/1,000, simplifying by dividing numerator and denominator by 1,000 would not be correct since 177 is not divisible by 1,000.

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

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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{16}{90}

\newline

(B)

\frac{17}{100}

\newline

(C)

\frac{8}{45}

\newline

(D)

\frac{177}{1,000}

Convert to fraction: Convert $0.1(7)$ to a fraction. Since $0.1(7)$ means $0.177777...$ , let $x = 0.177777...$ Multiplying by $100$ , we get $100x = 17.7777...$ Subtracting the original $x$ from this, $100x - x = 17.7777... - 0.177777...$ results in $99x = 17.6$ . Solving for $x$ gives $0.1(7)$ $0$ .
Simplify fraction: Simplify the fraction $17.6/99$ . Since $17.6$ can be written as $176/10$ , the fraction becomes $176/990$ . Simplifying by dividing numerator and denominator by $2$ , we get $88/495$ .
Check option (A): Check each option to see if it simplifies to $\frac{88}{495}$ . For (A) $\frac{16}{90}$ , simplifying by dividing numerator and denominator by $2$ gives $\frac{8}{45}$ .
Check option (B): For (B) $\frac{17}{100}$ , this fraction is already in its simplest form and does not equal $\frac{88}{495}$ .
Check option (C): For (C) $\frac{8}{45}$ , this was obtained from simplifying $\frac{16}{90}$ , which we already found to be equivalent to $\frac{88}{495}$ .
Check option (D): For (D) $\frac{177}{1,000}$ , simplifying by dividing numerator and denominator by $1,000$ would not be correct since $177$ is not divisible by $1,000$ .