1988 AMC 12 第 10 题

Question

在一次实验中，测得某科学常数

C

为

2.43865

，误差至多为

\pm0.00312

。实验者希望公布一个每一位都可靠的

C

值。也就是说，无论

C

的实际值是多少，把

C

舍入到所公布的位数时，都必须得到这个公布值。实验者能公布的最精确

C

值是

In an experiment, a scientific constant

C

is determined to be

2.43865

with an error of at most

\pm0.00312.

The experimenter wishes to announce a value for

C

in which every digit is significant. That is, whatever

C

is, the announced value must be the correct result when

C

is rounded to that number of digits. The most accurate value the experimenter can announce for

C

is

2

2.4

2.43

2.44

2.439

求出

C

的最小和最大可能值

Find the smallest and largest possible values of

C

将两个端点依次舍入到越来越多位有效数字

Round both endpoints to increasing numbers of significant digits

可能区间为

[2.43553,2.44177]

。其中每个数舍入到三位有效数字都是

2.44

，但两个端点舍入到四位有效数字时结果不同。因此，能保证正确的最精确公布值是

2.44

。

所以正确答案是 D。

The possible interval is

[2.43553,2.44177].

Every number in it rounds to

2.44

at three significant digits, but the endpoints round differently at four significant digits. Hence

2.44

is the most accurate guaranteed announcement.

Thus the correct answer is D.

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