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Tutor's Blog

20 Days to Go(-10 Days) Approximation and Errors

April 6, 2018

問題1:

The volume of a pack of lemon tea is350 ml. It is qualified if the percentage error of volume is not more than 0.5%. Jessica claims that the total volume of 20 packs of qualified lemon tea can be 7.04 L correct to the 3 significant figures. Do you agree with her? Explain your answer briefly.
20 Days to Go(-10 Days) Approximation and Errors
Actual volume of 20 packs of temon tea<20×350×(1+0.5%)
Actual volume of 20 packs of temon tea<7035 ml
Consider the lower limit of the measurement 7.04L,
(7.04−0.005)×1000=7035 ml
Since the Actual volume of 20 packs of temon tea
It is impossible to have this measurement.

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20 Days to Go(-10 Days) Approximation and Errors
這個問題同學仔有三點要留意。
1. 關於percentage error(在past paper 上不見其蹤影，但在practice paper 上卻出了一題)，同學仔要記得
20 Days to Go(-10 Days) Approximation and Errors
而且，upper limit 同lower limit 分別係將measured value 加同減去maximum absolute error。
所以我們可以將measured value×(1+percentage error)=upper limit
2. 關於upper and lower limit，同學仔要留意actual value 係可以去到lower limit，但去唔到upper limit。所以個range of the measurement 會係 7035 ml ≤the measurement<7045 ml
3. 關於兩個量度的可行性比較。我們應該將兩者的範圍都搵出來，然後比較有沒有重疊的部分。係呢題入面，
20×350×(1−0.5%)≤Actual volume of 20 packs of temon tea<20×350×(1+0.5%)
⇒6965≤Actual volume of 20 packs of temon tea<7035
另一方面
7035≤the measurement<7045
20 Days to Go(-10 Days) Approximation and Errors
同學仔可以從上圖中見到，兩者並無重疊的地方。
20 Days to Go(-10 Days) Approximation and Errors

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