Which fractions are equivalent to 0.{63}? Select all that apply. Multi-select Choices: (A)63/99 (B)7/11 (C)6/11 (D)63/100

Convert to Fraction: Step 1: Convert 0.{63} to a fraction. 0.{63} means 0.636363..., which is a repeating decimal. To convert it to a fraction, let x = 0.636363... Then, 100x = 63.636363... Subtracting these, 99x = 63 So, x = 63/99.Simplify Fraction: Step 2: Simplify 63/99. The greatest common divisor (GCD) of 63 and 99 is 9. Divide both numerator and denominator by 9: 63 ÷ 9 = 7, 99 ÷ 9 = 11. Thus, 63/99 simplifies to 7/11.Check Options: Step 3: Check each option. (A) 63/99 is equivalent to 7/11, which we found is equivalent to 0.{63}. (B) 7/11 is the simplified form of 63/99, so it is equivalent. (C) 6/11 needs to be checked. To check, convert 6/11 to a decimal: 6 ÷ 11 ≈ 0.545454..., which is not 0.636363... (D) 63/100 as a decimal is 0.63, which is not repeating like 0.636363...

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Which fractions are equivalent to $0.\overline{63}$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $\frac{63}{99}$ $\newline$ (B) $\frac{7}{11}$ $\newline$ (C) $\frac{6}{11}$ $\newline$ (D) $\frac{63}{100}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

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Q. Which fractions are equivalent to

0.\overline{63}

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

\frac{63}{99}

\newline

(B)

\frac{7}{11}

\newline

(C)

\frac{6}{11}

\newline

(D)

\frac{63}{100}

Convert to Fraction: Step $1$ : Convert $0.\overline{63}$ to a fraction. $\newline$ $0.\overline{63}$ means $0.636363...$ , which is a repeating decimal. $\newline$ To convert it to a fraction, let $x = 0.636363...$ $\newline$ Then, $100x = 63.636363...$ $\newline$ Subtracting these, $99x = 63$ $\newline$ So, $x = \frac{63}{99}.$
Simplify Fraction: Step $2$ : Simplify $\frac{63}{99}$ . The greatest common divisor (GCD) of $63$ and $99$ is $9$ . Divide both numerator and denominator by $9$ : $63 \div 9 = 7$ , $99 \div 9 = 11$ . Thus, $\frac{63}{99}$ simplifies to $\frac{7}{11}$ .
Check Options: Step $3$ : Check each option. $\newline$ (A) $\frac{63}{99}$ is equivalent to $\frac{7}{11}$ , which we found is equivalent to $0.\{63\}$ . $\newline$ (B) $\frac{7}{11}$ is the simplified form of $\frac{63}{99}$ , so it is equivalent. $\newline$ (C) $\frac{6}{11}$ needs to be checked. $\newline$ To check, convert $\frac{6}{11}$ to a decimal: $6 \div 11 \approx 0.545454...$ , which is not $0.636363...$ $\newline$ (D) $\frac{63}{100}$ as a decimal is $\frac{7}{11}$ $0$ , which is not repeating like $0.636363...$