The decimal representation of $\frac{7}{2^3 \cdot 5^4}$ will have how many digits after the decimal point?

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{29}{343}$

The decimal expansion of $\frac{9}{1600}$ will terminate after $\ldots \ldots \ldots \ldots$ digits.

$A$ positive integer is of the form $3q + 1$,where $q$ is a natural number. Can you write its square in any form other than $3m + 1$,i.e.,$3m$ or $3m + 2$ for some integer $m$? Justify your answer.

Consider the numbers $4^{n}$,where $n$ is a natural number. Check whether there is any value of $n$ for which $4^{n}$ ends with the digit zero.

The form of any odd positive integer $a$ is .......... where $m$ is some integer.