For the decimal expansion of a rational number $\frac{p}{q}$ to be terminating,if $q = 2^m \cdot 5^n$,then $m, n \in$ . . . . . . ($R$,$N \cup \{0\}$,$Z$)

In the decimal representation of $\frac{7}{80}$,how many digits will be there after the decimal point?

Prove that the square of every integer is of the form $3m$ or $3m+1$,where $m \in \mathbb{Z}$.

Write down the decimal expansion of the rational number $\frac{23}{2^{3} 5^{2}}$.

$(3k+2)^2$ leaves remainder ............ on dividing by $3$.

$A$ 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.