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Convert 2.56 56 being repeated to a fraction

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Final answer:

To convert the repeating decimal 2.56 56 to a fraction, multiply it by 100 and subtract the original decimal to eliminate the repeating part. Then, solve the resulting equation to find the fraction form of the repeating decimal.


Step-by-step explanation:

To convert the decimal number 2.56 56 (repeated) to a fraction, we can use the concept of infinite geometric series. Let x represent the repeating decimal. We multiply x by 100 to eliminate the decimal places. Subtracting x from the product, we get a new number that has the repeating part shifted by two decimal places. Hence, 100x - x = 256. We can solve this equation to find the value of x.

100x - x = 256 99x = 256 Now, x = \frac{256}{99}


Learn more about Converting repeating decimals to fractions

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