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$What is 0.6 bar(62) as a fraction? Move numbers to the blanks to complete the fraction. ◻ 79 125 313 457 495 632 999$

What is $0.6 \overline{62}$ as a fraction? Move numbers to the blanks to complete the fraction. $\newline$ $\square$ $\newline$ $79$ $\newline$ $125$ $\newline$ $313$ $\newline$ $457$ $\newline$ $495$ $\newline$ $632$ $\newline$ $999$

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Math Problems

Grade 6

Convert between percents, fractions, and decimals: word problems

Full solution

Q. What is

0.6 \overline{62}

as a fraction? Move numbers to the blanks to complete the fraction.

\newline

\square

\newline

79

\newline

125

\newline

313

\newline

457

\newline

495

\newline

632

\newline

999

Understand notation of repeating decimal: Understand the notation of the repeating decimal. $0.6\overline{62}$ means that the decimal is $0.6626262\ldots$ , where the digits $\text{“}62\text{”}$ repeat indefinitely.
Let $x$ be decimal: Let $x$ be the repeating decimal $0.\overline{62}$ . $\newline$ $x = 0.\overline{62}$
Multiply by $100$ : Multiply $x$ by $100$ to shift the repeating digits two places to the left. $\newline$ $100x = 66.2\overline{62}$
Subtract to eliminate repetition: Subtract the original $x$ from $100x$ to get rid of the repeating part. $\newline$ $100x - x = 66.2\overline{62} - 0.6\overline{62}$ $\newline$ $99x = 65.6$
Solve for x: Solve for x. $\newline$ $x = \frac{65.6}{99}$
Simplify fraction by factors: Simplify the fraction by looking for common factors. $\newline$ Both the numerator and the denominator are divisible by $11$ . $\newline$ $x = (65.6 / 11) / (99 / 11)$ $\newline$ $x = 5.96 / 9$
Convert decimal to fraction: Further simplify the fraction by converting the decimal in the numerator to a fraction. $\newline$ $5.96$ can be written as $\frac{596}{100}$ . $\newline$ $x = \frac{\frac{596}{100}}{9}$ $\newline$ $x = \frac{596}{9 \times 100}$ $\newline$ $x = \frac{596}{900}$
Further simplify fraction: Simplify the fraction by looking for common factors again. $\newline$ Both the numerator and the denominator are divisible by $4$ . $\newline$ $x = (\frac{596}{4}) / (\frac{900}{4})$ $\newline$ $x = \frac{149}{225}$
Look for common factors: Check if the fraction can be simplified further. $149$ and $225$ have no common factors other than $1$ , so the fraction is in its simplest form.