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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.
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.
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
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
同學仔可以從上圖中見到，兩者並無重疊的地方。
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超研教育專注優質數學教育，以舒適學習方案令學生學好數學。課程針對數學考試常見題型加以分析，釐清數理概念，建立及提升解題解難能力，令學生處理多變的試題更有優勢。
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