Which fractions are equivalent to 0.{45}? Select all that apply. Multi-select Choices: (A)9/20 (B)5/11 (C)45/99 (D)45/100

Identify decimal as fraction: Identify the repeating decimal 0.{45} as a fraction. To convert a repeating decimal to a fraction, let x = 0.454545... Multiply x by 100 (since the repeating part has two digits), so 100x = 45.454545... Subtract x from 100x: 100x - x = 45.454545... - 0.454545... This simplifies to 99x = 45. Convert decimal to fraction: Solve for x by dividing both sides by 99: x = 45 / 99. Simplify the fraction 45/99 by dividing the numerator and the denominator by their greatest common divisor, which is 9. So, 45/99 = 5/11.

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Which fractions are equivalent to $0.\overline{45}$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $\frac{9}{20}$ $\newline$ (B) $\frac{5}{11}$ $\newline$ (C) $\frac{45}{99}$ $\newline$ (D) $\frac{45}{100}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Which fractions are equivalent to

0.\overline{45}

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

\frac{9}{20}

\newline

(B)

\frac{5}{11}

\newline

(C)

\frac{45}{99}

\newline

(D)

\frac{45}{100}

Identify decimal as fraction: Identify the repeating decimal $0.\overline{45}$ as a fraction. $\newline$ To convert a repeating decimal to a fraction, let $x = 0.\overline{45}$ . Multiply $x$ by $100$ (since the repeating part has two digits), so $100x = 45.\overline{45}$ . Subtract $x$ from $100x$ : $100x - x = 45.\overline{45} - 0.\overline{45}$ . This simplifies to $99x = 45$ .
Convert decimal to fraction: Solve for $x$ by dividing both sides by $99$ : $x = \frac{45}{99}$ . Simplify the fraction $\frac{45}{99}$ by dividing the numerator and the denominator by their greatest common divisor, which is $9$ . So, $\frac{45}{99} = \frac{5}{11}$ .