Question

what is the decimal form of \\(dfrac{17}{150}\\)? \\(0.overline{13}\\) \\(0.overline{1}\\) \\(0.11\\) \\(0.11overline{3}\\)

Explanation:

Step1: Divide 17 by 150

To convert the fraction $\frac{17}{150}$ to a decimal, we perform the division: $17 \div 150$.
First, we know that $150 \times 0.1 = 15$, so we subtract: $17 - 15 = 2$.
Now we bring down a zero (making it 20), but $150$ goes into $20$ zero times, so we add a decimal point and a zero, making it $200$.
$150 \times 1 = 150$, subtract: $200 - 150 = 50$.
Bring down a zero: $500$.
$150 \times 3 = 450$, subtract: $500 - 450 = 50$.
We see that the remainder $50$ repeats, so the decimal will have a repeating part.
Putting it all together: $17 \div 150 = 0.11\overline{3}$ (because after $0.11$, the $3$ repeats as we keep getting a remainder of $50$ which leads to $3$ in the decimal place).

Answer:

$0.11\overline{3}$ (the fourth option: $0.11\overline{3}$)