### Chap 3: Reasonable Estimation?

Textbook: Exercise 3.3 (p69)

(a) 5837 + 985 ≈ 7000
(b) 347 - 482 + 650 ≈ -500
(c) 23.92 x 4.801 ≈ 1200
(e) 62.47 x 0.093 ÷ 0.00217 ≈ 40000

• Write down if each estimated value is reasonable?
When you have completed with this piece of work, proceed to AceLearning to attempt the Quizzes 03 & 04 (as Homework). You should finish them by 2359h today :D

1. 5837+985≈7000 is reasonable as the numbers were rounded correctly and evaluated correctly.
347-482+650≈-500 is not correct as it is positive
c is incorrect as there is an extra 0
e is incorrect as it should be 3000

2. a) Yes.
5837 + 985 ≈ 6000 + 1000 ( 1 S.F. )
= 7000 (Ans)

b) Yes.
347 - 482 + 650 ≈ 300 - 500 + 700 ( 1 S.F. )
= 500 (Ans)

c) No.
23.92 x 4.801 ≈ 20 x 5 ( 1 S.F. )
= 100 ( Ans )

d) No.
62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.1 ÷ 0.002
= 6 ÷ 0.002
= 3000

Sorry if there was any errors done. : D

3. (a) 5837 + 985 ≈ 7000
5837 + 985
≈6000+1000
=7000
(b) 347 - 482 + 650 ≈ -500
347 - 482 + 650
≈300-500+700
=-200+700
=500
(c) 23.92 x 4.801 ≈ 1200
23.92 x 4.801
≈24 x 5
=120
d)62.47 x 0.093 ÷ 0.00217 ≈ 40000
62.47 x 0.093 ÷ 0.00217
≈62 x 0.1 ÷ 0.002
=6.2 ÷ 0.002
=0.013

4. a) It is reasonable. 6000 + 1000 ≠ 7000
b)It is not reasonable. It should be 300-500+700≠500 not -500
c) It is not reasonable. It should 24*5= 120 not 1200.
d) It is 60*0.1÷0.002≠3000 not 40000

5. a) It is definitely reasonable as the answer is correct
5837 + 985
≈ 6000 + 1000 (1 S.F.)
= 7000

b) It is not reasonable. its suppose to be 500, not (-500)
347 - 482 + 650
≈ 300 - 500 + 700 (1 S.F.)
= 500

c) It is not reasonable as the answer is 120, not 1200.
23.92 x 4.801
≈ 24 x 5 (1 S.F)
= 120

d) This is also unreasonable. It is 3000, not 40000.
62.47 x 0.093 ÷ 0.00217
≈ 60 x 0.1 ÷ 0.002 (1 S.F)
= 6 ÷ 0.002
= 3000

6. This comment has been removed by the author.

7. (a)Yes
5837+985
≈6000+1000
=7000

(b)No
347-482+650
≈300-500+650
=450

(c)No
23.92 x 4.801
≈24 x 5
=120

(e)No
62.47 x 0.093÷0.00217
≈62 x 0.09÷0.002
=2700

8. (a) Definitely yes!
5837 + 985 ≈ 6000 + 1000
= 7000
``````````````````````````````````````````````````
(b) No.
347 - 482 + 650 ≈ 300 - 500 + 700
= ( - 200 ) + 700
= 500. Not - 500
``````````````````````````````````````````````````
(c) No.
23.92 x 4.801 ≈ 24 x 5
= 120 . Not 1200
``````````````````````````````````````````````````
(e) No . 62.47 x 0.093 ÷ 0.00217 ≈ 62 x 0.09÷0.002
=2700 . Not 40000

9. (a) 5837 + 985 ≈ 7000
Yes because (a)5837+985≈6000+1000(1 S.F)=7000
(b) 347 - 482 + 650 ≈ -500
No, as 347-482+650≈300-500+700(1 S.F)=500
(c) 23.92 x 4.801 ≈ 1200
No, as 23.92 x 4.801≈24 x 5(1 S.F)=120
(e) 62.47 x 0.093 ÷ 0.00217 ≈ 40000
No,as 62.47 x 0.093÷0.00217≈62 x 0.09÷0.002(1 S.F)=2790

10. (a) 5837 + 985
≈ 6000 + 1000 (1sf)
= 7000
(correct 7000)

(b) 347 - 482 + 650
≈ 300 - 500 + 700 (1sf)
= 500
(wrong -500)

(c) 23.92 x 4.801
≈ 20 x 5 (1sf)
= 100
(wrong 1200)

(e) 62.47 x 0.093 ÷ 0.00217
≈ 60 x 0.09 ÷ 0.002 (1sf)
= 27000
(wrong 40000)

11. (a) 5837 + 985 ≈ 7000

It is reasonable. It is rounded off to 1 significant figure before it is worked out.

5837 + 985
≈ 6000 + 1000 (1 S.F.)
= 7000

(b) 347 - 482 + 650 ≈ -500

No, it is not reasonable. The answer should be 500 instead of -500 as the numbers are rounded to 2 significant figures.

347 - 482 + 650
≈ 350 - 500 + 650 (2 S.F.)
= -150 + 650
= 500

(c) 23.92 x 4.801 ≈ 1200

No, it is not reasonable. There is an extra 0 in the answer.

23.92 x 4.801
≈ 24 x 5.0 (2 S.F.)
= 120

(d) 62.47 x 0.093 ÷ 0.00217 ≈ 40000

No, it is not reasonable. The answer is too large.

62.47 x 0.093 ÷ 0.00217
≈ 60 x 0.09 ÷ 0.002 (1 S.F.)
= 2700

12. 5837 + 985≈ 6000 + 1000 (1sf)
=7000
This answer is perfectly correct as the estimation has been done correctly and answering has been done correctly.

347 - 482 + 650≈ 300 - 500 + 700(1sf)
=-200 + 700
= 500
The first answer was wrong as there is not supposed to be a negative sign in the last answer. This is what the working and answer should be like.

23.92 x 4.801≈ 24 x 5(1sf)
= 120
There is a extra 0 at the end of the answer in the evaluation given. This is how it should be done.

62.47 x 0.093 ÷ 0.00217≈ 60 x 0.09 ÷ 0.002
= 5.4 ÷ 0.002
= 2700
The first answer given had only been rounded off after the evaluation. This is the correct one.

13. (a) 5837 + 985 ≈ 7000

5837 + 985 ≈ 6000 + 1000 (1 S.F)
= 7000

The estimation is correct as it had been rounded off correctly, and there were no calculation errors, and the symbols are done correctly.
(b) 347 - 482 + 650 ≈ -500

347 - 482 + 650 ≈ 300 - 500 + 700 (1 S.F.)
= -200 + 700
= 500

The estimation is correct as it had been rounded off correctly, but the final answer is wrong. Negative - Positive, and negative is lesser than positive, we should follow the positive sign, so the correct answer should be 500 and not -500.

(c) 23.92 x 4.801 ≈ 1200

23.92 x 4.801 ≈ 20 x 5 (1 S.F)
= 100

the estimation is wrong. To get a final answer as 1200, the number has to be about 35 x 35. But here, when we round off, it goes to 20 and 5. There is a lot of difference so the answer is obviously not correct.

(e) 62.47 x 0.093 ÷ 0.00217 ≈ 40000

62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.09 ÷ 0.002 (1 S.F)
= 5.4 ÷ 0.002
= 2700

14. (a) is correct.
(b) is wrong as 300-500+700 (1 S.F.)= 500, which is positive and not negative.
(c) is wrong as there is an extra zero.
(d) is wrong as 62x0.09÷0.002=2790
≈2700

15. (a) 5837 + 985 ≈ 7000

5837 + 985(1SF)
≈6000 + 1000
=7000

(b) 347 - 482 + 650 ≈ -500

347 - 482 + 650(1SF)
≈300 - 500 + 650
=450

(c) 23.92 x 4.801 ≈ 1200

23.92 x 4.801(1SF)
≈20 x 5
=100

(e) 62.47 x 0.093 ÷ 0.00217 ≈ 40000

62.47 x 0.093 ÷ 0.00217(1SF)
≈60 x 0.09 ÷ 0.002
=2700

16. (a) 5837 + 985 ≈ 7000(1.S.F) Is reasonable

(b)347 - 482 + 650 ≈ -500 is not resonable, it should be:
347 - 482 + 650 ≈ 300-500+700(1.S.F)
= 500

(c)23.92 x 4.801 ≈ 1200 is not reasonable, it should be:
23.92 x 4.801 ≈ 20 x 5(1.S.F)
= 100

(e) 62.47 x 0.093 ÷ 0.00217 ≈ 40000 is not reasonable, it should be:
62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.9÷ 0.002(1.S.F)
=2700

17. (a) Is reasonable

(b) (wrong)347 - 482 + 650
≈ 300 - 500 + 700 (1S.F)
=100

(c) (wrong)23.92 x 4.801
≈ 20 x 5
= 100

(e) (wrong) 2.47 x 0.093 ÷ 0.00217
≈ 60 x 0.9 ÷ 0.002 (1.S.F)
=2700

18. a) Yes.
5837 + 985 ≈ 6000 + 1000(1SF)
= 7000

b) Yes.
347 - 482 + 650 ≈ 300 - 500 + 700(1SF)
= 500

c) No.
23.92 x 4.801 ≈ 20 x 5(1SF)
= 100

e) No.
62.47 x 0.093 ÷ 0.00217 ≈ 60 x 0.1 ÷ 0.002
= 6 ÷ 0.002
= 3000

19. (a) Yes.
5837 + 985
≈ 6000 + 1000 (1 S.F.)
= 7000

(b) Yes.
347 - 482 + 650
≈ 300 - 500 + 700 (1 S.F.)
= -500

(c) No.
23.92 x 4.801
≈ 20 * 5 (1 S.F)
= 100, not 1200

(e)
62.47 x 0.093 ÷ 0.00217
≈ 60 * 0.09 ÷ 0.002 (1 S.F)
= 2700, not 40000

-Christopher Nah
(Sorry for handing in late!) :(