Write the repeating decimal as a fraction. .844844844 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits ＂844＂ repeat indefinitely.Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.844844844...Isolate Repeating Part: To isolate the repeating part, we can multiply x by 1000, since there are three digits in the repeating sequence: 1000x = 844.844844...Subtract Decimal Part: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 844.844844... - 0.844844844...Solve for x: Performing the subtraction, we get: 999x = 844Simplify Fraction: Now, we solve for x by dividing both sides of the equation by 999: x = 844 / 999We can simplify the fraction by looking for a common divisor. Both 844 and 999 are divisible by 1, but we need to check if there's a larger common divisor to simplify the fraction further.Upon checking, we find that there is no common divisor greater than 1 for 844 and 999. Therefore, the fraction is already in its simplest form. x = 844 / 999

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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.

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.844844844

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits $\text{“}844\text{”}$ repeat indefinitely.
Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.844844844...$
Isolate Repeating Part: To isolate the repeating part, we can multiply $x$ by $1000$ , since there are three digits in the repeating sequence: $1000x = 844.844844\ldots$
Subtract Decimal Part: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 844.844844... - 0.844844844...$
Solve for x: Performing the subtraction, we get: $999x = 844$
Simplify Fraction: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{844}{999}$
Simplify Fraction: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{844}{999}$ We can simplify the fraction by looking for a common divisor. Both $844$ and $999$ are divisible by $1$ , but we need to check if there's a larger common divisor to simplify the fraction further.
Simplify Fraction: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{844}{999}$ We can simplify the fraction by looking for a common divisor. Both $844$ and $999$ are divisible by $1$ , but we need to check if there's a larger common divisor to simplify the fraction further.Upon checking, we find that there is no common divisor greater than $1$ for $844$ and $999$ . Therefore, the fraction is already in its simplest form. $x = \frac{844}{999}$