chapter 9 i standard form enhance

8/10/2019 Chapter 9 I Standard Form ENHANCE

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Chapter 9 STANDARD FORM

1.1 Significant Figures

Important concepts

Round off the foo!ing num"ers correct to the num"er of significant figures indicated !ithin

the "rac#ets.

64 349 (3)

$% &'' ( & significant figures )

707.2 (2)

*1' ( + significant figures)

0.064 34 (3)

'.'$%& ( & significant figures )

7.072 (2)

*.1 ( + significant figures )

,-ampes ,-ercises

Round off the foo!ing num"ers correct to the gi/en significant figures.

Standard Form 135

4


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1.+ Standard Form

1.+ a. ,-pressing Num"ers in Standard Form

Important Concept

n standard form a number is ritten as

$0n

A

here $0$


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if the decima !oint is moed to the eft, nis a positi/einteger.

if the decima !oint is moed to the right, nis a negati/einteger.

ST,0 &+ rite the number in the form ' $0n

,-ampe

$. $ 6 & $. 6 $03

-te! $ + /orm the number, '.

oe the decima !oint & steps to the eft. ence, A 3 1.$

-te! 2 + btain the aue of n.8he decima !oint is moed & steps to the eft, hence n is positi/eand

n3 &.

-te! 3 + rite the number in the form ' $0n

, hence 1.$ 1'3

2. 0.0 0 0 0 5 4 6 & 5.46 5$0

-te! $ + /orm the number, '.oe the decima !oint 5 ste!s to the right. ence, A 3 2.%$

-te! 2 + btain the aue of n.8he decima !oint is moed 2 steps to the right, hence n is negati/eand

n3 2.

-te! 3 + rite the number in the form ' $0n

, hence 2.%$ 1' 5

:;-+

$. *!ress each of the fooing in standard form

a) 293204

$0932.2 =

a) 30 657 &b)

3$0942.$24$9 = b) 345&

c)2

$0,9.77,9 = c) 2$0 & d)$

$029.39.32 = d) 76.$&

e)0

$032.532.5 = e) =7,.6 f)$

$072.6672.0

= c) =57,.0

g) 2

$043.$0$43.0

= g) =0996.0 h)3

$066.600665.0

= h) =00,93.0

i)4$0,.70007,.0 = i) =00032$.0 =)

5$05.,0000,5.0

= =) =0000992.0

Standard Form 137


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8he smaer inde* is ad=usted to e>ua the bigger inde* beforeaddition or subtraction is !erformed.

2. Con/ert each of the foo!ing to a singe num"er.

a) 6,5$0$0,5$.6

4=

a)

= 4

$0,74.5 b) 322$$022$.3

3=

b)=

3

$0902.$

c) 5.76,$06,5.7 2

= c) = 2$006$.$ d) 53.,,$0,53.,

$= d) =

$$0,0$.4

e) 00$.6$000$.6 0

= e) = 0$006,.7 f) 5,6$.0$0,6$.5

$=

f) = $$02$,.2

g) 0600,.0$000,.6 2

=

g) = 2$0655.9 h) 00245.0$045.2

3=

h) = 3$03$9.6

i) 000376.0$076.3 4

=

i) = 4$063.5 =) 0000673.0$073.6

5=

=)5

$042.9

1.+" Operations in/o/ing Standard Form

1.+1 Addition and Su"traction

,-ampes ,-ercises

auate each of the fooing, giing anser in standard form

Standard Form 138


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a)43

$0$.,$05.4 +

4$3

$0$.,$045.0 += +

44

$0$.,$045.0 +=

4$0)$.,45.0( +=

4

$055., =

a)43

$0$.7$03.2 +

b)34

$04.7$02.2

+

3$4

$04.7$022.0 +

+=

33

$04.7$022.0

+=

3$0)4.722.0( +=

3

$062.7 =

b)34

$07.3$02.7

+

c)23

$0$.,$05.7

$23

$0,$.0$05.7 +

=

3$0),$.05.7( =

3

$069$.6 =

c)23

$03.7$05.9

d)43

$03.7$04.9

$43

$073.0$04.9 +

=

33

$073.0$04.9

=

3$0)73.04.9( =

3

$067., =

d)43

$02.9$02.7

1.++ Mutipication and Di/ision

,-ampes ,-ercises

,/auate each of the foo!ing 4 gi/ing 5our ans!er in standard form

Standard Form 139

a))$0()$0( nm BA

nmBA

+ $0)( b) )$0()$0(

nmBA

nmA $0


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a)26

$06.3$04 26$0)6.34( +=

,

$04.$4 =

9

$044.$ =

a)26

$03.4$05

b)24

$02$07.5

24$0)27.5( +=

2$04.$$ =

$

$0$4.$ =

b)24

$04$05.3

c)42

$03$02.6

42$0)32.6( =

6$06.$, =

5

$0,6.$ =

c)42

$04$0$.7

d)2

5

$02

$07.,

25$0

2

7., =

3

$035.4 =

d)5

,

$02

$02.$

e)5

2

$04

$02.7

52

$04

2.7 +=

3

$0,.$ =

e)5

7

$03

$07.,

f)5

6

$09

$03.6

56$0

9

3.6 +=

$

$07.0 =

2$07

=

f)5

6

$0,

$06.5

Standard Form 140


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g) 600

$03 6

2

6

$06$03

=

26$0

6

3 =

,

$05.0 =

9

$05

=

g) 5000

$06 3

,6AMINATION FORMAT 78,STIONS

$. ;ound off 6 24 correct to 2

significant figures.

' 6 200 6 290

B 6 20 ? 6 300

2. ;ound off $0726 correct to 2


' $$00 $0700

B $0000 ? $0

3. ;ound off 2.673 correct to 3


' 2.6 2.7

B 2.67 ? 2.70

4. ;ound off 0.00035$$ correct to 3


' 0.00035$ 0.0035$2

B 0.00035$$ ? 0.000352$

5. ;ound off 0.036 correct to to significant

figures.

'. 0.03 0.04

B. 0.036 ?. 0.037

6. = 4$0,4.3

' 00003,4.0 3,40

B 0003,4.0 ? 3,4000

7. = 5$002.$

' $02 $0200

B $020 ? $02000

. = 4$0,4.3

' 00003,4.0 3,40

B 0003,4.0 ? 3,4000

9. *!ress 0.000072 in standard form.

'$

$02.7

4$02.7

B2

$02.7 ?

5$02.7

$0. *!ress 55000 in standard form.

'

3$05,.5

5$05,.5

B

4$05,.5 ?

6$05,.5

Standard Form 141


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-

;@

2$00.3

$$. =+ 66000$06.2 5

'5

$026.3 5

$0,6.6

B9

$026.3 ?9

$0,6.6

$2. =+ $3$2 $07.2$0,.4

'$2

$0$,.3 $2

$05.7

B$3

$0$,.3 ?$3

$05.7

$3. = 65

$02.3$035.6

'5

$0$2.3

5$003.6

B6

$0$2.3 ?

6$003.6

$4. = 7700000$04.9 6

'5

$07.$ 5

$063.,

B6$07.$ ?

6$063.,

$5 = 6$059.4

'7

$045.2 9

$045.2

B,

$045.2 ?$0

$045.2

$6. = $0$2

$04$04.5

'$

$0$6.2 3

$0$6.2

B2

$0$6.2 ?4

$0$6.2

$7.=

4$07

09.0

'6

$04.$

2$04.$

B2

$04.$ ?

6$04.$

$.=

004.0

$004.3$4

'$3

$060.7 $5

$060.7

B$4

$060.7 ?$6

$060.7

$9.( )

=

22

$07

7,40

'5

$0$2.$ 5

$06.$

B6

$0$2.$ ?6

$06.$

20.=

3$04$6

2000

'$

$000.5

4$0$3.3

B$

$000.5 ?4

$0$3.3

2$. ; $.36 miions is to be shared b" four

!eo!e. *!ress the anser in standard

form.

'. 3.4 * $015

. 340 * $0 B. 3.4 * $04 ?. 3.40 * $05

22.

cm

3

$04

Diagram 1

n the ?iagram $,PQRS is a rectange.

8he area, in2

cm , of the rectange is

'6

$02.$ 4

$0$2.0

B6

$0$2 ?5

$02.$

23. n assan has5

$00$.$ acres of and.

e ants to diide his and e>ua" among

Standard Form 142


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his chidren. acuate the and area, in

acres, that each of n assanAs chidren

gets.

'4

$03.$ 5

$0$.,

B5

$03.$ ?6

$0$.,

24. 8he s!eed of ight is gien as$,

$03

ms .

acuate the time, in seconds, ight taes to

trae .$03 $0

m

'2

$02.$ 3

$03.,

B2

$02.$ ?

3$03.,

S0M 0ast ear 7uestions

S0M +''& (No/em"er)

$ ;ound off 0.036 correct to to significant

figures.

'. 0.003

B. 0.04

. 0.036

?. 0.037

2 = 4$027.6

'. 0.0000627

B. 0.000627

. 62 700

?. 6 270 000

3. =+ ,,000$0,.$ 5

'5

$06,.2

B9

$06,.2

5

$006.$

9$0

4. 8he area of a rectanguar nurser" !ot is2

Bm2.7 . ts idth is 2400 m. 8he

ength, in m, of the nurser" !ot is

'3

$03

B4

$03

3

$0,.4

?4

$0,.4

S0M +''% (:une)

$ ;ound off $0 75 correct to three


' $0 00 $0 70

B $0 0 ? $0 900

Standard Form 143


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2 -tate 7. 06 $05as a singe number.

' 70 600 7 060 000

B 706 000 ? 70 600 000

3 8he ength of a ree of red thread is $.3 $06

mm and the ength of a ree of bue thread is

65000 cm. acuate the tota ength, in cm, of

one ree of red thread and four rees of bue

thread.

' $.56 $05 3.9 $0

5

B 2.73 $05 ? 7. $0

5

43

$04

0002.0

&

' 5 $0 ,

5 $0 7

B 5 $0 2

? 5 $0 $

S0M +''% ( NO;,M


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'. 0.007564 . 0.000007564

B. 0.00007564 ?. 0.0000007564

3=

0000005

03.0

'3

$06 ,

$06

B4

$06 ?9

$06

S0M +''$ (NO;,Muare of side

20 cm. acuate the number of ties re>uired

to coer the foor fu".

'4$0,.$

4$06.3

B,

$0,.$ ?,

$06.3

S0M +''* (:une)

$ ;ound off 0.0526 correct to three


'. 0.0527 . 0.053

B. 0.0526 ?. 0.052

2 *!ress4

$0564.7 as a singe number.

'. 75 640 000 . 0.0007564

B. 75 640 ?. 0.00007564

3.9$0

$0$.2$03., &

'9$02.6

9$009.,

B$0

$02.6 ?$0

$009.,

4. a 'bu has a rectanguar garden. 8he ength of

the garden is 45 m and its idth is 20m. a 'bu

ants to encose his garden ith a ire fence.

acuate the tota ength, in cm, of the ire fence

re>uired.

'3

$05.6 4

$00.9

B4

$03.$ ?5$06.3

S0M +''* (NO;,M


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'gricutura one ndustria one

m$05 4

00 cm

500 cm

S0M +'' (:une)

$ ;ound off $57 correct to three


'. $5 . $50

B. $6 ?. $60

2 -tate4$006.4 as singe number.

'. 4 060 . 406 000

B. 40 600 ?. 4 060 000

345

$02.$$0$.6 & .

'4

$090.4 5$090.4

B4

$09,.5 ?5

$09,.5

4 ?iagram $ shos a rectange re!resenting an

agricutura one and a s>uare re!resenting an

industria one.

acuate the area, in m2, of the agricutura

one

'.,

$0,4.$ .7$04

B.7

$0,4.$ ?.6$04

S0M +'' (NO;,M


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ANS=,RS

ha!ter 9+ Standard Form

$.$

$.2

$ a)3$0657.3 b) 3$045,.3

Standard Form 147

1 sf + sf & sf

2 0000 0000 0500

4 3000 3$00 3070

6 500 5$0 507

20 2$ 20.6

$0 3 3.5 3.47

$2 0.3 0.30 0.300

$4 0.03 0.033 0.0330

$6 0.000 0.0000 0.00000

$ 0.00006 0.000064 0.0000644

20 0.00004 0.00004$ 0.00004$0


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c)2

$0$.2 d)$

$06$.7

e)0

$07,.6 f)$

$07,.5

g)2

$096.9 h)

3$093.,

i)4

$02$.3 =)

5$092.9

2a) 5 740 b) $902

c) $06.$ d) 4.0$

e) 7.06 f) 0.22$

g) 0.09655 h) 0.0063$9

i) 0.00563 =) 0.0000942

1.+1

$a)4

$033.7 b) $902c) $06.$ d) 4.0$

e) 7.06 f) 0.22$

g) 0.09655 h) 0.0063$9

i) 0.00563 =) 0.0000942

2a)4

$033.7 b)3

$042.4

c)3

$077., d)3

$02,.6

1.++

a)9

$0$5.2 b)$

$040.$

c)5

$0,4.2 d)

2$000.6

e)2

$09.2 f)

2$000.7

g)6

$02.$

,6AMINATION FORMAT 78,STIONS

1 D + < &

chapter 9 i standard form enhance

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