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What is \newline0.632‾0.6\overline{32} as a fraction? Move numbers to the blanks to complete the fraction.\newline□79\frac{\Box}{79}\newline□125\frac{\Box}{125}\newline□313\frac{\Box}{313}\newline□457\frac{\Box}{457}\newline□495\frac{\Box}{495}\newline□632\frac{\Box}{632}\newline□999\frac{\Box}{999}

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Convert between percents, fractions, and decimals: word problemsright chevron icon

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Q. What is \newline0.632‾0.6\overline{32} as a fraction? Move numbers to the blanks to complete the fraction.\newline□79\frac{\Box}{79}\newline□125\frac{\Box}{125}\newline□313\frac{\Box}{313}\newline□457\frac{\Box}{457}\newline□495\frac{\Box}{495}\newline□632\frac{\Box}{632}\newline□999\frac{\Box}{999}
  1. Understand repeating decimal notation: Understand the notation of the repeating decimal. 0.632‾0.6\overline{32} means that the decimal is 0.6323232…0.6323232\ldots, where the digits 3232 repeat indefinitely.
  2. Define variable xx: Let xx be the repeating decimal 0.60.6 bar(3232).\newlineSo, x=0.6323232…x = 0.6323232\ldots
  3. Shift decimal by multiplying by 100100: Multiply xx by 100100 to shift the decimal two places to the right, aligning the repeating digits.\newline100x=63.2323232…100x = 63.2323232\ldots
  4. Eliminate repeating part by subtraction: Subtract the original xx from 100x100x to eliminate the repeating part.\newline100x−x=63.2323232...−0.6323232...100x - x = 63.2323232... - 0.6323232...\newline99x=62.699x = 62.6
  5. Solve for x: Solve for x by dividing both sides of the equation by 9999.\newlinex=62.699x = \frac{62.6}{99}
  6. Convert mixed number to improper fraction: Convert the mixed number 62.662.6 to an improper fraction.62.6=62+0.6=62+610=62+3562.6 = 62 + 0.6 = 62 + \frac{6}{10} = 62 + \frac{3}{5}Now, convert 6262 to a fraction with a denominator of 55.62=62×(55)=310562 = 62 \times \left(\frac{5}{5}\right) = \frac{310}{5}So, 62.6=3105+35=(310+3)/5=313562.6 = \frac{310}{5} + \frac{3}{5} = \left(310 + 3\right)/5 = \frac{313}{5}
  7. Divide by 9999 using reciprocal: Now, we have x=3135x = \frac{313}{5} divided by 9999.\newlineTo divide by 9999, we multiply by the reciprocal of 9999, which is 199\frac{1}{99}.\newlinex = (3135)×(199)\left(\frac{313}{5}\right) \times \left(\frac{1}{99}\right)
  8. Multiply numerators and denominators: Multiply the numerators and denominators. \newlinex=313×1/(5×99)x = 313 \times 1 / (5 \times 99)\newlinex=313/495x = 313 / 495

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