Estimation and Approximation

7/25/2019 Estimation and Approximation

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ESTIMATION AND APPROXIMATION

1. (a) Evaluate 21.6

28.3 using a calculator.

(b) Round off your answer in (a) to

(i) 1 significant figure,

(ii) the nearest integer.

ns! (a) """""""""""""""""""""#1$

(b) (i) """""""""""""""" #1$

(ii) """""""""""""""" #1$

2. (a) %se your calculator to evaluate the following e&'ressions, giving your answers

correct to 3 significant figures.

(i)

312( 3

)+

(ii)

31

1 *12

8*

+

) Esti+ate the value of

*,.-1, -.,22

2.*12 3.(62

and correct the answer to the nearest integer.

ns! (a) (i) #1$

(ii) #1$

(b) #2$

3. E&'ress -.-6666 to

(i) the nearest thousandths,(ii) 2 deci+al 'laces,(iii) 3 significant figures.

ns! (i) #1$

(ii) #1$

(iii)


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#1$

*.(a)

howing your +ethod clearly, esti+ate the value of,.*

1-1

, giving your answer correct to

1 significant figure.(b) E&'ress 3* s/uare centi+etres in s/uare +etres.

(c) 0onvert 36 +h to +s.

ns! (a) #2$

(b) +2 #1$

(c) +s #2$

. Evaluate

(i) 3,.-6,22-8., 2 +, giving your answer correct to 2 significant

figures,#1$

(ii)

31

2 1

4

56

1

3

7

8

3

, giving your answer correct to 2 deci+al 'laces.

#1$


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6. (a)

E&'ress

81

1,

as a recurring deci+al.(b) ence round off your answer in (a) to

(i) 3 deci+al 'laces(ii) 3 significant figures

Answe

r

(a)44444444444 #1$

(b) (i) 4444444. #1$

(ii) 4444444. #1$

7. (a)0orrect -.--68 to

(i) 3 significant figures,

(ii) * deci+al 'laces.

(b)tate the nu+ber of significant figures in

(i) 12.32-,

(ii) 3--.

Answer(a)(i)44..4444444.

(ii)444444444..

(b)(i)4444444444

(ii)4444444.44..

#1$

#1$

#1$

#1$

%sing a

calculator,

evaluate each of

the following,

giving your

answers correct

8. Esti+ate, correct to one significant figure, the value of

3

*2.1 2.63

8 *.-21

.

Answer 444444..444444. #3$


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9. to

3 significant

figures.

(a)

-3

1

,

16*

32

+

,

(b)

22.-

.1223,

+

.

Answer (a)444444..4444444

(b)4444444.444444..

#2$

#2$

1-. E&'ress (a) 68 2* correct to nearest 1---.

(b) 2.* correct to 3 deci+al 'laces

(c) -.-123* correct to 3 significant figures

nswer (a) 4444444444 #1$

(b)4444444444. #1$

(c)44444444444 #1$

11. (a) An integer is estimated as 2---if it is rounded off to 1, 2or 3significant figures

respectively.

(i) Find the maximum possible value of the integer.

(ii) Find the minimum possible value of the integer

(b) Estimate the value of(62.3-1*(.3

12).2*(,,.8

correct your answer to the nearest integer.


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.

(a)(i).1!

(a)(ii).1!

(b). "!

1"

.

(a)

(b)

#se your calculator to evaluate the following.

(i)

22.136*.13

3-12.-

+ $ giving your answer correct to 2decimal places.

(ii)

),

*3(

13

21

3

1

1

$ giving your answer correct to % significant figures.

Estimate the value of( 7.02

2

5.99

2

+ 3.01) x

3 --1.12,

.

&ive your answer to one significant figure.

"

!

"

!

"

!

(c) 'rs ich wants to put tiles on the floor of her rectangular itchen$

measuring *.+, m by 1-.-%" m. he tiles will cost /%1.0+ per suare

metre. Estimate the amount of money 'rs ich will need to tile the floor.

&ive your answer correct to the nearest hundred dollars. %

!


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13. (a) E&'ress 83 -.3-* correct to(i) 2 deci+al 'laces,(ii) 3 significant figures.

(b) Esti+ate the value of

( )

%

"

"2.++1 "0.-"

".---1 -.++,

, giving your answercorrect to one significant figure.

Answer (a)(i)4....44444.4 #1$

(ii)444....444.4 #1$

(b)44...444444... #2$

1*. %se your calculator to evaluate

(i)

"

3

-.%2.--0,-1.-%+

"*

+, #2$


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(ii) , #2$

giving both the answers correct to 3 significant figures.

1. 5ithout using the calculator, esti+ate, correcting your answer to 1 significant figures, the value

of!

37.99724.906849.5346

nswer! #2$

16. (a) Esti+ate the following to 2 significant figures!(i) 26.3(ii) -.--3

(b) Hence, esti+ate the value of-,-3(.-

(3.2)6

to 1 significant figure.

ns(a)(i)"""""""""""""#1$

3

%

1-"22

33"%

"

+

2

1"3

""2

+

.

)(.


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(ii) """"""""""""#1$

ns(b)"""""""""""""""#1$

1. %se a calculator to find the value of.612.*,.1--8.,

23

giving your

answer correct to 3 significant figures.

ns(a)"""""""""""""""""""""""""""#2$

18. Round off the following.

a 383.-21 to * significant figures,

b 8.2 g to the nearest 1-- g.

nswer! (a) """"""""""""""""""""""" #1$

(b) """"""""""""""""""""""" #1$1. Evaluate the following.

a.221.

.332.18 2

, giving your answer correct to 3 deci+al 'laces,

b)

2

1)

31

),.(-33.*

+

, giving your answer correct to 3 significant figures.

nswer! (a) """"""""""""""""""""""" #1$

(b) """"""""""""""""""""""" #1$


9/13

2-.

Esti+ate, without the use of a calculator, the value of

3

2

-12.28

1.1138.6

, giving your

answer correct to 1 significant figure. how your woring clearly.#*$

21. Evaluate the following, giving your answer correct to 2 deci+al 'laces.

"

% )+1.2(

3

11)"%2.1(1"*

+

nswer! """""""""""""""""""" #2$

22. resha buys * 'ens at *8 cents and 6 files at 72. each at the school boosho'. hesho'ee'er ass for 716.-. how, by using esti+ation, that the sho'ee'er has +adea +istae. nd, write your e&'lanation in words on the lines below.


10/13

nswer! he sho'ee'er has +ade a +istae because """"""""""""""""""""""""

""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" #2$

23. E&'ress the following nu+bers to the degree of accuracy stated.

(a) -.-*6 correct to the nearest hundredth.

(b))12.13)

correct to the nearest integer.

(a) """"""""""""""""""""" #1$(b) """"""""""""""""""""" #1$

2*. Round off 21.3 to(a) 1 deci+al 'lace(b) 3 significant figures

nswer! (a) """"""""""""""""" #1$

(b) """"""""""""""""" #1$

2. (a) E&'ress, correct to 2 significant figures!(i) .

(ii) 26.88(iii) 3.-18

(b)

ence, esti+ate the value of

-18.3

88.26,. 3

.


11/13

ns!

(a)(i) #1$

(ii) #1$

(iii) #1$

(b) #2$

26. (a) Esti+ate the following to 2 significant figures

(i) 25475,

(ii) 1.*-,

(iii) -.--*8.

(b) Hence, esti+ate the value of

2,*), 1.*((-

-.-,-*8 1--

+ to 1 significant figure.

Answer: (a) (i)444444444444#1$

(ii)444444444444. #1$

(iii)444444444444. #1$

(b).44.44..44444444.....#2$


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11) a Express$ correct to " significant figures4

i ,1,."23ii 3.-2%

b 5ence estimate$ correct to 1 significant figure$ the value of

i ,1,."23 x 3.-2%

ii-2%.3

"23.,1,

Answer4 (a)(i) 66666666666666666666 1!

(ii)66666666666666666666 1!

(b)(i) 66666666666666666666 1!

(ii)66666666666666666666 1!


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Estimation and Approximation