Is it correct to say that the number $\frac{343}{2\times 7\times 5^2}$ has a non-terminating and repeating decimal expansion?

Without actually performing the long division, state whether the rational number $\frac{125}{44}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether the rational number $\frac{23}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether the rational number $\frac{129}{2^2\times 5^7\times 7^{17}}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Write down the decimal expansion of the rational number $\frac{3}{8}$ by writing its denominator in the form $2^m\times 5^n,$ when $m, n$ are non-negative integers.

Write down the decimal expansion of the rational numbers $\frac{7}{80}$ by writing their denominator in the form $2^m\times 5^n,$ when $m, n$ are non-negative integers.

Write down the decimal expansion of the rational number $\frac{14588}{625}$. [By converting the denominator in the form $2^m\times 5^n,$ when $m, n$ are non-negative integers]

Categorise the following as rational or irrational number. If it is rational of the form $\frac{a}{b}$, what can you say about prime factorisation of $b?$

$14.2312345$

Categorise the following as rational or irrational number. If it is rational of the form $\frac{a}{b}$, what can you say about prime factorisation of $b?$

$3.121012100121000121\dots$