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Sobee
0.6+0. bar(7)+0. bar(47)

Sobee $0.6+0 . \overline{7}+0 . \overline{47}$

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Add and subtract decimals

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Q. Sobee

0.6+0 . \overline{7}+0 . \overline{47}

Convert to Fraction: question_prompt: What is the sum of $0.6$ , $0.\overline{7}$ , and $0.\overline{47}$ ?
Add Fractions: First, let's convert $0.\overline{7}$ to a fraction. Since $7$ is the repeating digit, we can call it $x$ : $x = 0.\overline{7}$ . Then, $10x = 7.\overline{7}$ . Subtracting these two equations, we get $9x = 7$ , so $x = \frac{7}{9}$ .
Add Decimal and Fraction: Now, let's convert $0.\overline{47}$ to a fraction. Let $y = 0.474747...$ $\newline$ Then, $100y = 47.474747...$ $\newline$ Subtracting the two equations, we get $99y = 47$ , so $y = \frac{47}{99}$ .
Add Decimal and Fraction: Now, let's convert $0.\overline{47}$ to a fraction. Let $y = 0.474747\ldots$ $\newline$ Then, $100y = 47.474747\ldots$ $\newline$ Subtracting the two equations, we get $99y = 47$ , so $y = \frac{47}{99}$ . Now we add the fractions $\frac{7}{9}$ and $\frac{47}{99}$ . To do this, we need a common denominator. The common denominator for $9$ and $99$ is $99$ . So we convert $\frac{7}{9}$ to $y = 0.474747\ldots$ $1$ . Now we can add $y = 0.474747\ldots$ $1$ and $\frac{47}{99}$ to get $y = 0.474747\ldots$ $4$ .
Add Decimal and Fraction: Now, let's convert $0.\overline{47}$ to a fraction. Let $y = 0.474747\ldots$ $\newline$ Then, $100y = 47.474747\ldots$ $\newline$ Subtracting the two equations, we get $99y = 47$ , so $y = \frac{47}{99}$ . Now we add the fractions $\frac{7}{9}$ and $\frac{47}{99}$ . To do this, we need a common denominator. The common denominator for $9$ and $99$ is $99$ . So we convert $\frac{7}{9}$ to $y = 0.474747\ldots$ $1$ . Now we can add $y = 0.474747\ldots$ $1$ and $\frac{47}{99}$ to get $y = 0.474747\ldots$ $4$ . Finally, we add the decimal $y = 0.474747\ldots$ $5$ to the fraction $y = 0.474747\ldots$ $4$ . To make it easier, let's convert $y = 0.474747\ldots$ $5$ to a fraction, which is $y = 0.474747\ldots$ $8$ or $y = 0.474747\ldots$ $9$ or $100y = 47.474747\ldots$ $0$ . To add it to $y = 0.474747\ldots$ $4$ , we need a common denominator, which is $100y = 47.474747\ldots$ $2$ . So we convert $100y = 47.474747\ldots$ $0$ to $100y = 47.474747\ldots$ $4$ . Now we can add $100y = 47.474747\ldots$ $4$ and $y = 0.474747\ldots$ $4$ (which is also $100y = 47.474747\ldots$ $7$ ).

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