百分法(二)3.51
在步驟 2,當我們把應課稅入息實額分成多個部分時,就如把水逐一
倒進 5 個水箱般,而每個的容量依次如下:
■ 50 000 mL,■ 50 000 mL,■ 50 000 mL,■ 50 000 mL,■ 沒有限制
在以上情況,我們只用了 4 個水箱。事實上,我們有時不需使用全
部 5 個水箱。同理,我們不一定要把應課稅入息實額分成 5 個部分。 170 000 mL
= 50 000 mL + 50 000 mL +
50 000 mL + 20 000 mL + 0 mL
◀
德宏的應課稅入息實額是 $266 000,求他應繳的薪俸
稅。
圖解說明
考慮應課稅入息實額。 $50 000
$50 000
$50 000
$50 000
$66 000
程度一
例例 22
解
20 000 mL
50 000 mL
50 000 mL
50 000 mL
0 mL
(滿) (滿) (滿)
(一些)
(空)
這裏有 170 000 mL 水。我會先把水倒進
第一個水箱。當它注滿後,水會倒進 第二
個水箱⋯⋯然後是 第三個水箱⋯⋯
11.8 第 11 章
(a) 把 2 084 下捨入至最接近的十位。
(b) 把 3.69 下捨入至最接近的整數。
(c) 把 1.038 6 下捨入至二位小數。
2
即時訓練即時訓練
➥ 習題 11B 1, 2
II. 上捨入法
一般來說,當把一個數上捨入至某位後,我們可得出一個大於該數
的估計值。參看以下例子。
考慮 4 625.39 這個數。
把 4 625.39 上捨入至
步驟: 最接近的百位 一位小數
① 辨別要上捨入的數字。 4 625.39 4 625.39
② 把該數字加 1。
③ 對於該數字右方的各個數字,若它
(i) 在小數點前,把它改為「0」作為補位;
(ii) 在小數點後,把它刪去。
4 700 4 625.4
把「 6」加 1 把「 3」加 1
補位數字
(a) 把 1 732 上捨入至最接近的十位。
(b) 把 16.47 上捨入至最接近的整數。
(c) 把 3.094 上捨入至一位小數。
程度一
例例 3
Numerical Estimation 11.11
D Using Larger and Smaller Estimated Values
In some situations, not every estimation strategy can give a valid result.
For example, we may have to decide which strategy, rounding down or
rounding up, is more suitable to the given situation.
e.g. (i) The maximum load of a lift is 700 kg. The weights of 3 items
are 233 kg, 144 kg and 276 kg. Can the lift carry the 3 items at
the same time?
< <
233 kg
280 kg
150 kg
240 kg
276 kg
670 kg 700 kg
144 kg
actual
total weight
estimated
total weight
rounding up
maximum load
By rounding up each weight to the nearest 10 kg,
total weight . (240 + 150 + 280) kg
= 670 kg
1 700 kg
` The lift can carry the 3 items at the same time.
(ii) Kathy has to write a short story of at least 250 words. Her story
consists of 4 paragraphs of 38, 81, 106 and 52 words. Does
Kathy's story meet the total number of words required?
38
81
106
52
30
80
100
50
260
250
actual total
number of
words
estimated
total number
of words
rounding down
required
total number
of words
> >
By rounding down each number to the nearest 10,
total number of words . 30 + 80 + 100 + 50
= 260
2 250
` Kathy's story meets the total number of words required.
Please refer to the Enrichment
Topic 'More about Numerical
Estimation Strategies' in
Appendix I on P.A8.
◀
Numerical Estimation 11.11
D Using Larger and Smaller Estimated Values
In some situations, not every estimation strategy can give a valid result.
For example, we may have to decide which strategy, rounding down or
rounding up, is more suitable to the given situation.
e.g. (i) The maximum load of a lift is 700 kg. The weights of 3 items
are 233 kg, 144 kg and 276 kg. Can the lift carry the 3 items at
the same time?
< <
233 kg
280 kg
150 kg
240 kg
276 kg
670 kg 700 kg
144 kg
actual
total weight
estimated
total weight
rounding up
maximum load
By rounding up each weight to the nearest 10 kg,
total weight . (240 + 150 + 280) kg
= 670 kg
1 700 kg
` The lift can carry the 3 items at the same time.
(ii) Kathy has to write a short story of at least 250 words. Her story
consists of 4 paragraphs of 38, 81, 106 and 52 words. Does
Kathy's story meet the total number of words required?
38
81
106
52
30
80
100
50
260
250
actual total
number of
words
estimated
total number
of words
rounding down
required
total number
of words
> >
By rounding down each number to the nearest 10,
total number of words . 30 + 80 + 100 + 50
= 260
2 250
` Kathy's story meets the total number of words required.
Please refer to the Enrichment
Topic 'More about Numerical
Estimation Strategies' in
Appendix I on P.A8.
◀
8
3 資料形象化 (Data Visualization)
不同類型的圖表,具體呈現抽象的數學概念。
將薪俸稅「稅階」的概念形象化
3A冊 第3章 • 第3.51頁
以圖表有系統地顯示
上捨入法的步驟
1B冊第11章 • 第11.8頁
將上捨入法和下捨入法估算的
概念形象化
Book 1B Ch.11 • P.11.11