lets practice 3\nhow is $0.0\\overline{25}$ written as a fraction in simplest form?

Explanation:

Step1: Assign variable to the decimal

Let $x = 0.0\overline{25}$, which means $x = 0.0252525...$

Step2: Eliminate repeating decimals (first shift)

Multiply $x$ by 10 to move past the non-repeating decimal: $10x = 0.252525...$

Step3: Eliminate repeating decimals (second shift)

Multiply $10x$ by 100 (since 2 digits repeat): $1000x = 25.252525...$

Step4: Subtract to isolate $x$

Subtract $10x$ from $1000x$: $1000x - 10x = 25.252525... - 0.252525...$ $990x = 25$

Step5: Solve for $x$ as fraction

$x = \frac{25}{990}$

Step6: Simplify the fraction

Divide numerator and denominator by GCD 5: $\frac{25 \div 5}{990 \div 5} = \frac{5}{198}$

Answer:

$\frac{5}{198}$