The decimal representation of $35457 / 6250$ terminates after how many decimal places?

Show that one and only one out of $n, n+4, n+8, n+12$ and $n+16$ is divisible by $5,$ where $n$ is any positive integer.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{29}{343}$.

Why are the following numbers composite? Explain: $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$

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

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.