Write the repeating decimal as a fraction. .994994994 ______

Denote Decimal as x: Let's denote the repeating decimal 0.994994994... as x. x = 0.994994994... To convert this repeating decimal into a fraction, we will first express x in a way that isolates the repeating part. Multiply x by 1000 (since the repeating part has three digits) to shift the decimal point three places to the right. 1000x = 994.994994994...Convert to Fraction: Now, subtract the original number x from the result of the multiplication to eliminate the repeating decimals. 1000x - x = 994.994994994... - 0.994994994... This subtraction gives us: 999x = 994Solve for x: Now, we can solve for x by dividing both sides of the equation by 999. x = 994 / 999Simplify Fraction: The fraction 994/999 can be simplified. Both the numerator and the denominator have a common factor of 1, which does not change the value when divided. Therefore, the fraction is already in its simplest form. x = 994 / 999

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Write the repeating decimal as a fraction. $\newline$ $.994994994$

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Algebra 2

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.994994994

Denote Decimal as $x$ : Let's denote the repeating decimal $0.994994994\ldots$ as $x$ .
$x = 0.994994994\ldots$
To convert this repeating decimal into a fraction, we will first express $x$ in a way that isolates the repeating part.
Multiply $x$ by $1000$ (since the repeating part has three digits) to shift the decimal point three places to the right.
$1000x = 994.994994994\ldots$
Convert to Fraction: Now, subtract the original number $x$ from the result of the multiplication to eliminate the repeating decimals. $\newline$ $1000x - x = 994.994994994... - 0.994994994...$ $\newline$ This subtraction gives us: $\newline$ $999x = 994$
Solve for x: Now, we can solve for x by dividing both sides of the equation by $999$ . $\newline$ $x = \frac{994}{999}$
Simplify Fraction: The fraction $\frac{994}{999}$ can be simplified. Both the numerator and the denominator have a common factor of $1$ , which does not change the value when divided. Therefore, the fraction is already in its simplest form. $\newline$ $x = \frac{994}{999}$