Question

一个正方形的计算面积为 $1.1025$ 平方英寸，精确到万分之一平方英寸。该正方形边长的测量值有多少位有效数字？

The number of significant digits in the measurement of the side of a square whose computed area is $1.1025$ square inches to the nearest ten-thousandth of a square inch is:

$2$

$3$

$4$

$5$

$1$

答案：D

知识点：measurement error significant digits square root

难度评级：1810

小提示：

真实面积介于 $1.10245$ 平方英寸与 $1.10255$ 平方英寸之间

The true area lies from $1.10245$ up to $1.10255$ square inches

大提示：

对误差区间的两端开平方，观察边长有多少位数字保持不变

Take square roots of the error interval and see how many digits of the side are fixed

解答：

给出的面积表示真实面积满足 $1.10245\le A\lt1.10255\text{。}$ 两边开平方，近似得到 $1.049976\le\sqrt A\lt1.050024\text{。}$ 因此，任何可能的边长精确到万分之一时都舍入为 $1.0500$ 。小数点后的末尾零是有效数字，所以 $1.0500$ 有五位有效数字。

因此，正确答案是 D。

The reported area means the true area lies in $1.10245\le A\lt1.10255.$ Taking square roots gives approximately $1.049976\le\sqrt A\lt1.050024.$ Every possible side length therefore rounds to $1.0500$ to the nearest ten-thousandth. The trailing zeros after the decimal are significant, so $1.0500$ has five significant digits.

Thus, the correct answer is D.

1953 AMC 12 第 29 题

答案：D

难度评级：1810

小提示：

大提示：

解答：

其他年份的第 29 题