Final answer:
To convert a repeating decimal to a fraction, you can set up an equation and solve for x, which in this case equals 1/45.
Step-by-step explanation:
To convert the repeating decimal 0.02 (with the 2 repeating) to a fraction, we'll use a simple algebraic technique.
First, let x be your decimal, 0.0222... Then set up the equation 100x = 2.222... This represents the original number, but shifted two decimal places to the right.
Next, subtract the original equation from the second: 100x - x = 2.222... - 0.0222... This simplifies to 99x = 2.2. Solving for x, we find that x = 2.2/99, which simplifies to the fraction 2/90.
Always remember to simplify your fraction for the final answer. In this case, 2/90 can be simplified to 1/45.
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