Write the repeating decimal as a fraction. .055055055 ______

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal 0.055055055... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern is 055, which means the decimal can be written as 0.055055055...Represent as Variable: Let's represent the repeating decimal as a variable, say x. So, let x = 0.055055055...Isolate Repeating Part: To isolate the repeating part, we can multiply x by 1000, because the repeating part is three digits long. This gives us 1000x = 55.055055055...Subtract Decimals: Now, subtract the original x from 1000x to get rid of the decimal part. This gives us 1000x - x = 55.055055055... - 0.055055055...Solve for x: Perform the subtraction: 999x = 55. This is because the repeating decimals cancel each other out.Simplify Fraction: Now, solve for x by dividing both sides of the equation by 999. This gives us x = 55 / 999.Final Fraction: To simplify the fraction, we look for the greatest common divisor (GCD) of 55 and 999. The GCD of 55 and 999 is 1, so the fraction is already in its simplest form.Therefore, the repeating decimal 0.055055055... as a fraction is 55/999.

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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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.055055055

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal $0.055055055\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern is $055$ , which means the decimal can be written as $0.055055055\ldots$
Represent as Variable: Let's represent the repeating decimal as a variable, say $x$ . So, let $x = 0.055055055\ldots$
Isolate Repeating Part: To isolate the repeating part, we can multiply $x$ by $1000$ , because the repeating part is three digits long. This gives us $1000x = 55.055055055\ldots$
Subtract Decimals: Now, subtract the original $x$ from $1000x$ to get rid of the decimal part. This gives us $1000x - x = 55.055055055... - 0.055055055...$
Solve for x: Perform the subtraction: $999x = 55$ . This is because the repeating decimals cancel each other out.
Simplify Fraction: Now, solve for $x$ by dividing both sides of the equation by $999$ . This gives us $x = \frac{55}{999}$ .
Final Fraction: To simplify the fraction, we look for the greatest common divisor (GCD) of $55$ and $999$ . The GCD of $55$ and $999$ is $1$ , so the fraction is already in its simplest form.
Final Fraction: To simplify the fraction, we look for the greatest common divisor (GCD) of $55$ and $999$ . The GCD of $55$ and $999$ is $1$ , so the fraction is already in its simplest form.Therefore, the repeating decimal $0.055055055\ldots$ as a fraction is $\frac{55}{999}$ .