Quod Erat Demonstrandum

2013/01/10

誤差

Filed under: Junior Form Mathematics — johnmayhk @ 2:41 下午

某初中題

“The length of a cube is measured as 50 cm. If the measurement is correct to the nearest 10 cm, find the relative error in calculating the volume of the cube."

我隨便寫答案:

\frac{55^3-50^3}{50^3}

學生隨即問為何不是

\frac{50^3-45^3}{50^3}

呢?起初也有些疑惑,但再想清楚定義:

Relative error = (maximum absolute error)/measurement

55^3-50^3=4137550^3-45^3=33875 大,故 maximum absolute error 應取較大者。

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