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

Convert to fraction: Step 1: Convert 0.{63} to a fraction. 0.{63} means 0.636363..., a repeating decimal. To convert it to a fraction, let x = 0.636363... Multiplying by 100 (since the repeating part has two digits), we get 100x = 63.636363... Subtracting the original x from this, 100x - x = 63.636363... - 0.636363... results in 99x = 63. x = 63/99.Simplify fraction: Step 2: Simplify 63/99. The greatest common divisor (GCD) of 63 and 99 is 9. Dividing both numerator and denominator by 9, we get 63/99 = 7/11.Check options: Step 3: Check each option. (A) 7/11 is equivalent to 63/99, as calculated. (B) 6/11 is not equivalent because 6/11 = 54.545454... which is different from 0.636363... (C) 63/100 is not equivalent because 63/100 = 0.63, which is a terminating decimal and not repeating like 0.636363... (D) 63/99 is equivalent, as shown in Step 1.

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

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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{7}{11}

\newline

(B)

\frac{6}{11}

\newline

(C)

\frac{63}{100}

\newline

(D)

\frac{63}{99}

Convert to fraction: Step $1$ : Convert $0.\overline{63}$ to a fraction. $\newline$ $0.\overline{63}$ means $0.636363...$ , a repeating decimal. To convert it to a fraction, let $x = 0.636363...$ Multiplying by $100$ (since the repeating part has two digits), we get $100x = 63.636363...$ Subtracting the original $x$ from this, $100x - x = 63.636363... - 0.636363...$ results in $99x = 63$ . $x = \frac{63}{99}.$
Simplify fraction: Step $2$ : Simplify $\frac{63}{99}$ . The greatest common divisor (GCD) of $63$ and $99$ is $9$ . Dividing both numerator and denominator by $9$ , we get $\frac{63}{99} = \frac{7}{11}.$
Check options: Step $3$ : Check each option. $\newline$ (A) $\frac{7}{11}$ is equivalent to $\frac{63}{99}$ , as calculated. $\newline$ (B) $\frac{6}{11}$ is not equivalent because $\frac{6}{11} = 54.545454...$ which is different from $0.636363...$ $\newline$ (C) $\frac{63}{100}$ is not equivalent because $\frac{63}{100} = 0.63$ , which is a terminating decimal and not repeating like $0.636363...$ $\newline$ (D) $\frac{63}{99}$ is equivalent, as shown in Step $1$ .