Question

write the following decimal as a fraction of two integers in simplest form: (0.overline{55}) enter the answer check it

Explanation:

Step1: Assign variable to decimal

Let $x = 0.\overline{55}$, meaning $x = 0.5555...$

Step2: Eliminate repeating decimals

Multiply $x$ by 100 (since 2 digits repeat):
$100x = 55.5555...$

Step3: Subtract to isolate $x$

Subtract original $x$ from $100x$:
$100x - x = 55.5555... - 0.5555...$
$99x = 55$

Step4: Solve for $x$

$x = \frac{55}{99}$

Step5: Simplify the fraction

Divide numerator and denominator by GCD(55,99)=11:
$\frac{55\div11}{99\div11} = \frac{5}{9}$

Answer:

$\frac{55}{99}$ simplified to $\frac{5}{9}$