### Chap 3: Reasonable Estimation?

Textbook: Exercise 3.3 (p69)

(a) 5837 + 985 = (est) 7000

(b) 347 - 482 + 650 = (est) -500

(c) 23.92 x 4.801 = (est) 1200

(e) 62.47 x 0.093 ÷ 0.00217 = (est) 40000

• Write down if each estimated value is reasonable?

1. (a) 5837+ 985≈ (est)7000
(b)347-482+650≈ (est)500
(c)23.92x4.801≈ (est)120
(e)60x0.1÷0.002≈(est)3000

(b),(c) and (e) are wrong

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3. The estimated answers of b, c and e are unreasonable.

b should be 347-482+650≈300-500+700(1SF)
=500

c should be 23.92 X 4.801≈24X5 (1SF)
=120

e should be 62.47X0.093÷0.00217≈62X0.09÷0.002(1SF)
=2.835

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5. (a) 5837 + 985 ≈ 6000 + 1000
= 7000

Yes, (a) is reasonable.

(b) 347 - 482 + 650 ≈ 300 - 500 + 700
= -200 + 700
= -500

Yes, (b) is reasonable.

(c) 23.92 x 4.801 ≈ 24 x 5
= 120

No, (c) is not reasonable.

(e) 62.47 x 0.093 ÷ 0.00217 ≈ 62 x 0.09 ÷ 0.002
= 5.58 ÷ 0.002
= 2.790

No, (e) is not reasonable.

6. (a) 5837 + 985 = 6822 (reasonable)
(b) 347 - 483 + 650
≈ 135 + 650
515(not reasonable )
(c) 23.92 x 4.801 = 114.83992(not reasonable)
(d) 62.47 x 0.093 ÷ 0.00217 = 2 677 28571 (not reasonable)

7. (a)5837 + 985 = 6822 (reasonable)
(b)347 - 482 + 650
=-135 + 650
=515 (not reasonable)
(c)23.92 x 4.801
=114.83992 (not reasonable)
(d)62.47 x 0.093 ÷ 0.00217 = 2 677.28571 (not reasonable)

8. a)5837 + 985=(est) 6000 + 1000
= 7000
Therefore, the estimated value of (a) is reasonable.

b)347 - 482 + 650≈(est) 300 - 500 + 700
=(-200) + 700
=500
The estimated value of (b) is not reasonable; the answer should be (+)500 instead of -500.

c) 23.92 x 4.801≈(est) 20 x 5
=100
The estimated value of (c) is not reasonable; the answer is 100 instead of 1200.

e) 62.47 x 0.093 ÷ 0.00217≈(est) 60 x 0.09 ÷ 0.002
= 5.4 ÷ 0.002
=2700
The estimated value of (e) is not reasonable; the answer is 2700 instead of 40 000.

ALL answers are rounded off to the 1st significant number.

9. a)5837 + 985 ≈ 6000 + 1000
= 7000
b)Not reasonable because
347 - 482 + 650 ≈ 300 - 500 + 700
= 500
c) Not reasonable because
23.92 x 4.801 ≈24 x 4
=96
d)62.47 x 0.093 ÷ 0.00217 ≈ 62 x 0.1
= 6.2

10. No, (b), (c), and (e) is not reasonable. (a) is reasonable.

(a) 5837+985≈6000+1000
=7000

(b) 347-482+650

11. I think that (a) is reasonable as the sum is rounded off to the nearest thousands.
I think that (b) is unreasonable as the estimated answer is suppose to be 500(300-500+700) and not -500.
I think that (c) is unreasonable as the estimated answer is suppose to be 120(24x5) and not 1200.

12. a= Reasonable
6000+1000=7000
b=Unreasonable
400-500+700=500
c=Unreasonable
20x5=100
e=Unreasonable
60x0.09÷0.002=2700

13. a) 5837 + 985≈6000+1000
=7000
(b) 347 - 482 + 650≈300-500+700
=500
(c) 23.92 x 4.801≈20 x 5
=100
(e) 62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.09 ÷ 0.002
= 5.4 ÷ 0.002

14. (a) It is reasonable as the numbers are rounded off to 1 significant figure.
(b) It is unreasonable.
347 - 482 + 650 ≈ 300 - 500 + 700
= -200+700
= 500
The answer is not -500 but 500.
(c) 23.92 x 4.801 ≈ 20 x 5
= 100
(e) 62.47 x 0.093 0.00217 ≈ 60 x 0.09 ÷ 0.002
= 2790

15. (a) Exact value: 5837 + 985 = 6822 (reasonable)

(b) Exact value: 347-482+650 = 515 (not reasonable)

(c) Exact value : 23.92 x 4.801 = 114.83992 (not reasonable)

(d) 62.47 x 0.093 ÷0.00217 = 2677.28571 (not reasonable)

chengngee

16. a) reasonable

Working:

a) 5837+ 985 ≈ 6000+ 1000
= 7000

b) unreasonable

Working

b) 347-482+650 ≈ 300-500+700
= 500

Part 1

17. It is reasonable.
5837+985≈6000+1000
=7000
It is not reasonable.
347 - 482 + 650 ≈300-500+700
= 500
It is not reasonable.
23.92 x 4.801≈20×5
=100
62.47 x 0.093 ÷ 0.00217≈60×0.09÷0.002
= 2700

18. a) reasonable

5837+985≈6000+1000
=7000

b) reasonable
347-482+650≈ 300-500+700
= (-200) + 700
=-900

c) unreasonable

23.92 x 4.801≈ 24x5
=120

e) unreasonable

62.47x0.093÷0.00217≈ 62x0.1÷0.002
= 6.2÷0.002
= 3100

19. (a) 5837+985≈ 6000+1000
= (est)7000
(b) 347-482+650≈ 300-500+700
= (est) 500
(c) 23.92x4.801≈ 24x5
= (est) 120
(e) 62.47x0.093÷0.00217≈ 62x0.1÷0.002
= (est) 3100

(b), (c) and (e) are not reasonable.

20. Part 2

c) unreasonable

Workings:23.92x 4.801≈24x 5
=120

e) unreasonable

Workings: 62.47x0.093≈ 60x0.1÷0.002
=3000

21. (a) 5837 + 985 = (est) 7000
5837 + 985 ≈ 6000 + 1000
= 7000

(b) 347 - 482 + 650 = (est) -500
347 - 482 + 650 ≈300-500+700
= 500

(c) 23.92 x 4.801 = (est) 1200
23.92 x 4.801 ≈24 x 5
= 120

(e) 62.47 x 0.093 ÷ 0.00217 = (est) 40000
62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.09 ÷ 0.002
=2700

22. Follow-up:
(a) 5837 + 985 = 6822

(b) 347 - 482 + 650 = 515

(c) 23.92 x 4.801 ≈ 114

(e) 62.47 x 0.093 ÷ 0.00217 ≈ 2677

As comparing to the estimation, (a) is reasonable & (b),(c),(d) is not reasonable.

23. (a) is reasonable as both numbers are rounded off to 1 significant figure.
(b) It is not reasonable.
347-482+650≈-135+650
=515
(c) 23.92 x 4.801 ≈ 114(unreasonable)
(e) 62.47 x 00.093 ÷ 0.00217≈ 2677(unreasonable)