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5 problems match “terminating decimals”. Clear

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1. Odd reciprocals with terminating decimals ●●○○○ 20 ptsIf $\frac{a}{b}$ is the probability that the reciprocal of a randomly selected positive odd integer less than $2010$ gives a terminating decimal, with $a$ and $b$ relatively prime positive integers, find $a+b$.
2. Repeating decimals of n/30 ●●○○○ 20 ptsFor how many integers $n$ from $1$ to $29$ is the fraction $\frac{n}{30}$ a repeating decimal (that is, its decimal expansion does not terminate)?
3. Smallest multiple beyond 2010 with terminating decimals ●●○○○ 20 ptsLet $S$ be the set of all integers $k$ such that $\frac{17k}{66}$ and $\frac{13k}{105}$ are both terminating decimals. What is the smallest integer in $S$ that is greater than 2010?
4. Natural numbers with terminating quotients ●●●○○ 50 ptsFind all natural numbers $n \geq 2$ such that for every positive integer $k < n$, the quotient $\frac{n}{k}$ has a finite decimal representation (or is a whole number). List the values in increasing order.
5. Terminating decimals with nonzero hundredths digit ●●●○○ 50 ptsFor how many positive integers $n$ does $\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit?