Question

express (1.overline{5}) as a number in the form (\frac{a}{b}), where (a) and (b) are integers. select one answer a (\frac{3}{2}) b (\frac{14}{9}) c (\frac{8}{5}) d (\frac{10}{9})

Explanation:

Step1: Let $x$ equal the repeating decimal

Let $x = 1.\overline{5}$, which means $x = 1.555...$

Step2: Multiply to shift decimal right

Multiply $x$ by 10: $10x = 15.555...$

Step3: Subtract to eliminate repeating part

Subtract original $x$ from $10x$:
$$10x - x = 15.555... - 1.555...$$
$$9x = 14$$

Step4: Solve for $x$

Divide both sides by 9:
$$x = \frac{14}{9}$$

Answer:

D. $\frac{14}{9}$