Write the repeating decimal as a fraction. .033033033 ______

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Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern is 033, which repeats indefinitely after the decimal point.Express as Infinite Sum: Express the repeating decimal as an infinite sum of its repeating parts. Since the pattern 033 starts after the second decimal place, we can write it as: 0.033033033... = 0.033 + 0.00033 + 0.0000033 + ...Convert to Fractions: Convert each term in the sum into a fraction. The first term is 33/1000, the second term is 33/100000, and so on. This gives us: 0.033033033... = 33/1000 + 33/100000 + 33/10000000 + ...Recognize Geometric Series: Recognize that the sum forms a geometric series with the first term a_1 = 33/1000 and the common ratio r = 1/100.Use Sum Formula: Use the formula for the sum of an infinite geometric series, which is a_1 / (1 - r), to write the repeating decimal as a fraction. Substitute a_1 = 33/1000 and r = 1/100 into the formula. Sum = (33/1000) / (1 - 1/100)Simplify Expression: Simplify the expression by finding a common denominator and performing the division. Sum = (33/1000) / (99/100) Sum = (33/1000) * (100/99)Multiply Numerators and Denominators: Multiply the numerators and denominators to get the fraction. Sum = (33 * 100) / (1000 * 99) Sum = 3300 / 99000Reduce to Simplest Form: Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 3300. Sum = 3300 / 99000 = 1/30

Write the repeating decimal as a fraction. $\newline$ $.033033033$

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Write the repeating decimal as a fraction.\newline.033033033.033033033.033033033

Write the repeating decimal as a fraction. $\newline$ $.033033033$