AMC8 2000

AMC8 2000 · Q3

AMC8 2000 · Q3. It mainly tests Fractions, Inequalities with integers (floor/ceiling basics).

How many whole numbers lie in the interval between $\frac{5}{3}$ and $2\pi$?

区间$\frac{5}{3}$和$2\pi$之间有多少个整数？

(A) 2 2

(B) 3 3

(D) 5 5

(E) infinitely many 无数个

Answer

Correct choice: (D)

正确答案：（D）

Solution

The smallest whole number in the interval is $2$ because $5/3$ is more than $1$ but less than $2$. The largest whole number in the interval is $6$ because $2\pi$ is more than $6$ but less than $7$. There are five whole numbers in the interval. They are $2$, $3$, $4$, $5$, and $6$, so the answer is $\boxed{\text{(D)}\ 5}$.

区间最小整数是$2$，因为$\frac{5}{3} \approx 1.666$大于$1$小于$2$。最大整数是$6$，因为$2\pi \approx 6.28$大于$6$小于$7$。区间内有$2,3,4,5,6$五个整数，所以答案是$\boxed{\text{(D)}\ 5}$。

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