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Which fractions are equivalent to 0.45‾0.\overline{45}? Select all that apply.\newlineMulti-select Choices:\newline(A) 920\frac{9}{20}\newline(B) 45100\frac{45}{100}\newline(C) 4599\frac{45}{99}\newline(D) 511\frac{5}{11}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which fractions are equivalent to 0.45‾0.\overline{45}? Select all that apply.\newlineMulti-select Choices:\newline(A) 920\frac{9}{20}\newline(B) 45100\frac{45}{100}\newline(C) 4599\frac{45}{99}\newline(D) 511\frac{5}{11}
  1. Convert to Fraction: Step 11: Convert 0.45‾0.\overline{45} to a fraction.\newline0.45‾0.\overline{45} means 0.454545…0.454545\ldots repeating. To convert this repeating decimal to a fraction, let x=0.454545…x = 0.454545\ldots\newline100x=45.454545…100x = 45.454545\ldots\newlineSubtracting these equations:\newline100x−x=45.454545…−0.454545…100x - x = 45.454545\ldots - 0.454545\ldots\newline99x=4599x = 45\newlinex=4599x = \frac{45}{99}
  2. Simplify Fraction: Step 22: Simplify the fraction 4599\frac{45}{99}. The greatest common divisor (GCD) of 4545 and 9999 is 99. 45÷9=545 \div 9 = 5 99÷9=1199 \div 9 = 11 So, 4599\frac{45}{99} simplifies to 511\frac{5}{11}.
  3. Check Equivalent Fractions: Step 33: Check the choices for equivalent fractions.\newline(A) 920\frac{9}{20} is not equivalent to 511\frac{5}{11}.\newline(B) 45100\frac{45}{100} simplifies to 920\frac{9}{20}, which is not equivalent to 511\frac{5}{11}.\newline(C) 4599\frac{45}{99} simplifies to 511\frac{5}{11}, which is equivalent.\newline(D) 511\frac{5}{11} is directly given and is equivalent.

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