Non-Terminating, Recurring Decimals in Rational Numbers

The decimal form of the rational number $\frac{100}{81}$ is 

For the decimal expansion $27.\overline{142857}$, decide whether it is rational or not. If it is rational, then find the prime factors of its denominator.

Without actually performing long division method, state whether $\frac{129}{2^2\times 5^7\times 7^5}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{17}{6}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

What can you say about the prime factors of the denominator of the rational number $43.\overline{123456789}$.

State whether the real number $2.8284271\dots$ is Rational Number / Irrational Number.

State whether $5.\overline{234}$ is Rational Number / Irrational Number.