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

Convert to Fraction: Step 1: Convert 0.{45} to a fraction. 0.{45} means 0.454545... repeating. To convert this repeating decimal to a fraction, let x = 0.454545... 100x = 45.454545... Subtracting these equations: 100x - x = 45.454545... - 0.454545... 99x = 45 x = 45 / 99Simplify Fraction: Step 2: Simplify the fraction 45/99. The greatest common divisor (GCD) of 45 and 99 is 9. 45 ÷ 9 = 5 99 ÷ 9 = 11 So, 45/99 simplifies to 5/11.Check Equivalent Fractions: Step 3: Check the choices for equivalent fractions. (A) 9/20 is not equivalent to 5/11. (B) 45/100 simplifies to 9/20, which is not equivalent to 5/11. (C) 45/99 simplifies to 5/11, which is equivalent. (D) 5/11 is directly given and is equivalent.

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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) $\frac{45}{100}$ $\newline$ (C) $\frac{45}{99}$ $\newline$ (D) $\frac{5}{11}$

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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{45}{100}

\newline

(C)

\frac{45}{99}

\newline

(D)

\frac{5}{11}

Convert to Fraction: Step $1$ : Convert $0.\overline{45}$ to a fraction. $\newline$ $0.\overline{45}$ means $0.454545\ldots$ repeating. To convert this repeating decimal to a fraction, let $x = 0.454545\ldots$ $\newline$ $100x = 45.454545\ldots$ $\newline$ Subtracting these equations: $\newline$ $100x - x = 45.454545\ldots - 0.454545\ldots$ $\newline$ $99x = 45$ $\newline$ $x = \frac{45}{99}$
Simplify Fraction: Step $2$ : Simplify the fraction $\frac{45}{99}$ . The greatest common divisor (GCD) of $45$ and $99$ is $9$ . $45 \div 9 = 5$ $99 \div 9 = 11$ So, $\frac{45}{99}$ simplifies to $\frac{5}{11}$ .
Check Equivalent Fractions: Step $3$ : Check the choices for equivalent fractions. $\newline$ (A) $\frac{9}{20}$ is not equivalent to $\frac{5}{11}$ . $\newline$ (B) $\frac{45}{100}$ simplifies to $\frac{9}{20}$ , which is not equivalent to $\frac{5}{11}$ . $\newline$ (C) $\frac{45}{99}$ simplifies to $\frac{5}{11}$ , which is equivalent. $\newline$ (D) $\frac{5}{11}$ is directly given and is equivalent.