Try to find the decimal expansions of $\frac{10}{3}$ and $\frac{11}{12}$. What do you observe about the repetition of the digits after the decimal point? [Page No. 57]

Doing the long division:

$\frac{10}{3}=3.3333\dots=3.\overline{3}$ (the bar means $3$ repeats forever, right from the start).

$\frac{11}{12} = 0.91666 \dots = 0.91\overline{6}$ (the digits $91$ appear once, then $6$ repeats forever).

Observation: both are non-terminating repeating decimals, but the repeating part starts in different places. In $\frac{10}{3}$ the repetition begins immediately after the point (a pure repeating decimal). In $\frac{11}{12}$ there are a couple of non-repeating digits first, then the repeating block (a mixed repeating decimal). Neither terminates, because their denominators (3, and $12 = 2^2 \times 3$) contain the prime 3, a prime other than 2 or 5.