Estimation in numbers and measurement

Form 1 MathematicsChapter 5

Lesson requirement Textbook 1A Workbook 1A Notebook (and folder)

Before lessons start Desks in good order! No rubbish around!

An estimation is a rough guess on the actual values.

It does not represent the real answer. In real life, we seldom bring a

calculator with us. So, we can use estimation to make some decisions.

To get a better estimation, we need some techniques to round off a number.

Consider the “unwanted” leftmost digit. If greater or equal to 5, add 1 to left digit next

to it. Otherwise, leave left digit next to it

unchanged.

E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86 Rounding off to nearest tenth digit (十分位 ) Rounding off to nearest unit ( 個位 ) Rounding off to nearest ten digit ( 十位 )

Rounding off to nearest tenth digit 21.29 + 15.78 + 30.97 + 3.24 + 5.86

21.3 + 15.8 + 31.0 + 3.2 + 5.9 = 77.2

Rounding off to nearest unit (or one) 21.29 + 15.78 + 30.97 + 3.24 + 5.86

21 + 16 + 31 + 3 + 6 = 77 Rounding off to nearest ten digit

21.29 + 15.78 + 30.97 + 3.24 + 5.86 20 + 20 + 30 + 0 + 10 = 80

The actual answer is 77.14

Consider the leftmost digit. Leave the first leftmost digit Other change to 0!

E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86

21.29 + 15.78 + 30.97 + 3.24 + 5.86 20.00 + 10.00 + 30.00 + 3.00 + 5.00= 20 + 10 + 30 + 3 + 5= 68 (Actual answer is 77.14)

Consider the “unwanted” digits. All change to 0 Add 1 to left digit next to them

E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86

Rounding up to nearest tenth digit Rounding up to nearest unit Rounding up to nearest ten digit

Rounding up to nearest tenth digit 21.29 + 15.78 + 30.97 + 3.24 + 5.86

21.3 + 15.8 + 31.0 + 3.3 + 5.9 = 77.3 Rounding up to nearest unit (or one)

21.29 + 15.78 + 30.97 + 3.24 + 5.86 22 + 16 + 31 + 4 + 6 = 79

Rounding up to nearest ten digit 21.29 + 15.78 + 30.97 + 3.24 + 5.86

30 + 20 + 40 + 10 + 10 = 110 Actual answer =77.14. All are over-

estimated.

Consider the “unwanted” digits. All change to 0 Leave all left digits next to them

unchanged

E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86

Rounding down to nearest tenth digit Rounding down to nearest unit Rounding down to nearest ten digit

Rounding down to nearest tenth digit 21.29 + 15.78 + 30.97 + 3.24 + 5.86

21.2 + 15.7 + 30.9 + 3.2 + 5.8 = 76.8 Rounding down to nearest unit (or one)

21.29 + 15.78 + 30.97 + 3.24 + 5.86 21 + 15 + 30 + 3 + 5 = 74

Rounding down to nearest ten digit 21.29 + 15.78 + 30.97 + 3.24 + 5.86

20 + 10 + 30 + 0 + 0 = 60 Actual answer =77.14. All are under-

estimated.

of Textbook 1A Class Practice

Page 200 of Textbook 1A Questions 3 – 6

Pages 93 - 94 of WB 1A Questions 1 - 4

SHW (I) Questions 1 - 8

Choose one approximate value which is close in value to all (or most) numbers

E.g. 21356 + 19587 + 22098 + 18657

+ 20485 + 19444 20000 x 6= 120000

Choose a pair of numbers which makes the calculation easier

E.g. 345678 9 360000 9= 40000

E.g. 0.2468 x 163 0.25 x 160= 40

To change the order of the arithmetic operations for easy calculation

Only for first x then E.g.

415

1205

45

9205

449205449205

Make some adjustments during or after arithmetic operations

E.g. 6432 x 7 Consider 6432 x 7 = (6000 +432) x 7 First, 6000 x 7 = 42000 Then, 432 x 7 3000

(400 x 7 = 2800 432 x 7 is close to 3000)

So, the answer is about 45000

of Textbook 1A Questions 7 – 12

Page 94 of WB 1A Questions 5 - 6

SHW (I) Questions 9 - 14

Lesson Get ready all the time!

Desk Be order all the time!

Extra Tutorial Final examination less than 50

SHW (I) 11 Jan (Fri)

OBQ & CBQ Next week

Enjoy the world of Mathematics!

Ronald HUI

Estimation in numbers and measurement

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