Example 1.3. Uranium fuel rod in nuclear reactor 核子反應爐內的鈾燃料棒 Before insertion 插入前, rod length 棒長 = 3.241 m After insertion 插入後, rod length 棒長 = 3.249 m.

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Presentation transcript:

Example 1.3. Uranium fuel rod in nuclear reactor 核子反應爐內的鈾燃料棒 Before insertion 插入前, rod length 棒長 = m After insertion 插入後, rod length 棒長 = m Q 問 : What is the increase in length 長度增加多少 ? A: m  m = m = 8 mm Accuracy 精確度 = 1 mm Error 誤差 =  m =  1 mm  Increase in length is 長度增加 8 mm ( 1 sig. dig. 1 個有效數字 ) Any intermediate results must have at least 1 extra sig. dig. to avoid rounding errors. 每個中介結果必需保留多一個有效數字才能避免四捨五入的誤差 Caclulator: apply round-off & truncation only at the end. 計算機 : 全部算完才四捨五入和捨棄非有效數字。

Significant Figures Significant figures (digits) of an integer: all digits between the leftmost & rightmost non-zero digits. Trailing zeros are ambiguous. of a real number: all digits except leading zeros. Examples: Numbers with 5 sig. dig. : , , , Caution: An integer sometimes denotes infinite accuracy (  sig. dig. ). e.g., 2 in the formulae C = 2  R & A =  R 2. Note: may be taken as having 10 sig. dig.

Accuracy & Significant Figures means  2.94 is between 1.6 & 1.8 Accuracy worsens after each calculation. Result has accuracy of the least accurate member.  /  : Number of significant digits = that of the least accurate member. + /  : result is rounded off to the rightmost common digit. i.e.or

Bridge = km ( accuracy = km ) Ramp = 65.4 m = km ( acc = km ) Overall length = km km = km Overall acc = km, error =  km  Overall length = km  = ( # sig. dig. = 6 ) R E = 6.37  10 6 m ( # sig. dig. = 3 ) 2  R E =  10 6 m Overall # sig. digits = 3  2  R E = 40.0  10 6 m

Example 1.3. Uranium fuel rod in nuclear reactor Before insertion, rod length = m After insertion, rod length = m Q: What is the increase in length? A: m  m = m = 8 mm Accuracy = 1 mm Error =  m =  1 mm  Increase in length is 8 mm ( 1 sig. dig. ) Any intermediate results must have at least 1 extra sig. dig. to avoid rounding errors. Caclulator: apply round-off & truncation only at the end.