Write the repeating decimal as a fraction. .744744744 ______

Identify repeating pattern: Identify the repeating pattern in the decimal. The repeating pattern is 744.Assign variable x: Let x equal the repeating decimal, so x = 0.744744744...Shift decimal point: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating pattern has three digits. This gives us 1000x = 744.744744...Subtract original x: Subtract the original x from 1000x to get rid of the repeating decimals. This gives us 1000x - x = 744.744744... - 0.744744744...Perform subtraction: Perform the subtraction: 1000x - x = 999x and 744.744744... - 0.744744744... = 744.Set up equation: Now we have the equation 999x = 744.Divide by 999: Divide both sides of the equation by 999 to solve for x. This gives us x = 744/999.Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of 744 and 999. The GCD of 744 and 999 is 3.Simplify fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction. This gives us x = (744/3)/(999/3).Write final fraction: Perform the division: 744/3 = 248 and 999/3 = 333.Write the simplified fraction: x = 248/333.

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Write the repeating decimal as a fraction. $\newline$ $.744744744$

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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

.744744744

Identify repeating pattern: Identify the repeating pattern in the decimal. $\newline$ The repeating pattern is $744$ .
Assign variable x: Let $x$ equal the repeating decimal, so $x = 0.744744744\ldots$
Shift decimal point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating pattern has three digits. This gives us $1000x = 744.744744\ldots$
Subtract original $x$ : Subtract the original $x$ from $1000x$ to get rid of the repeating decimals. This gives us $1000x - x = 744.744744\ldots - 0.744744744\ldots$
Perform subtraction: Perform the subtraction: $1000x - x = 999x$ and $744.744744\ldots - 0.744744744\ldots = 744$ .
Set up equation: Now we have the equation $999x = 744$ .
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ . This gives us $x = \frac{744}{999}$ .
Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of $744$ and $999$ . The GCD of $744$ and $999$ is $3$ .
Simplify fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction. This gives us $x = \frac{744/3}{999/3}$ .
Write final fraction: Perform the division: $744/3 = 248$ and $999/3 = 333$ .
Write final fraction: Perform the division: $744/3 = 248$ and $999/3 = 333$ .Write the simplified fraction: $x = \frac{248}{333}$ .