Quod Erat Demonstrandum

2008/09/26

中二數學問題之有效數字

Filed under: Junior Form Mathematics — johnmayhk @ 9:37 上午

派完測驗,粱同學問:

如果 x = 0.25 (correct to 2 significant figures)

那麼 x 的 maximum value(最大值)是多少?

嗯,因為數值被修訂到兩位有效,即 maximum absolute error(最大的絕對誤差)是 \frac{0.01}{2} = 0.005,所以,x 的最大值就是 0.25 + 0.005 = 0.255 了。

但梁同學不同意,他說,如果把 0.255 修訂到兩位有效,那麼應該是 x = 0.26 (correct to 2 significant figures),而不是題目的 0.25。所以粱同學在測驗時寫 maximum x = 0.254。

大家如何回應粱同學的疑問?

3 則迴響 »

  1. interesting question, and it is time to show whether one can teach students well or not…

    I think I will try to ask the student what happens if we correct 0.2541 to 2 sig. fig.
    then he should realize his answer, 0.254, is not the maximum value
    then carry on with 0.2542, 0.2543, …, 0.2549, 0.25499, 0.254999,…
    hopefully he can get a sense that x can be any value below 0.255

    迴響 由 Daniel — 2008/09/26 @ 10:13 上午 | 回覆

  2. 我想我們很難向現代的中二學生
    去解釋0.2549, 0.25499等概念
    因為他們所接觸的數學題
    為了方便
    其數值每每是整數
    更遑論向中二學生解釋
    為何x沒有maximum value吧
    哈哈

    迴響 由 皮旦 — 2008/09/26 @ 11:36 上午 | 回覆

  3. @Daniel

    That’s exactly the way I told the student 0.254 is not the max.

    @皮旦

    Perhaps the question is a question itself, it means the ‘least upper bound’, not ‘maximum’.

    迴響 由 johnmayhk — 2008/09/27 @ 10:46 上午 | 回覆


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