Name:

WEST SPRING SECONDARY SCHOOL

"THIRST FOR KNOWLEDGE"

( ) Class: Date:

WORKSHEET 6

Chapter 1: Indices and Standard Form

Standard Form

Very (arge and very small numbers are tedious to write. A system was developed to overcome this problem. It iscalled the Standard Form or Scientific Notation.

A number in Standard Form is in the form of:

A x 10n, where 1 A < 10 and n is an integer. ]-HM-. •WMMMMMM IMMMMH

Some examples are:

7.24x10" 1.258x10 -12 5.22x10-

Converting Ordinary Form to Standard Form

We live in a universe of different shapes and sizes.

1 Light Year(Distance travelled by light in 1 year)

Diameter of Sun

Diameter of Earth

Length of Great Wall of China

Height of a Soldier

Length of a mosquito

Length of a Red Blood Cell

Ordinary Notation

9 460 000 000 000 000 m

1 390 000 000 m

12700000m

6 400 000 m

1.7m

0.01 m

0.0 000 075 m

Standard Form

q.4&* r*

\-3ft x \# *

| . ?1 x lo1 ^

£-4- x \&^ ^

I .~\ x \O° r»

1 x /o"* rn

t-5 x 'o~6 ryi

Converting Standard Form to Ordinary Form(www.ace-learning.com.sg)

Height of Mount Everest

Length of a Marathon

Diameter of the Moon

Diameter of Jupiter

Length of a Bacterium

Size of a HIV

Radius of a Hydrogen Atom

xOfdiD cy loUtion

8.848xl03m

4.2195xl04m

8.48xl06m

1. 42984 xlO'm

2x lO~ 6 m

9xlO- 8m

2.5xl(Tum

rSUadawlFtapn-

5M£ r*

42 145 p

3A-$O 000 ryo

J4-2 %4 t>oo m

0- bbv 002. no

0- boo Cot? 0°[ rr\

0- OOP w 0*0 025 rn

Summary

The following tables state the differences in the conversion of numbers to Standard Form andhow lo recognise from Standard Form whether a number is greater or smaller than one.

Conversion of Number to Standard Form

Size of Number — Directional Shift of Result on Index of :Decimal Point-; :- Base;10 wtthiadh.shift ;

HBMKwA*l**t **^«.^%MP8^3CS!-«ii'.-fiBiE*-it,uxW£&iivii*F-^ki-i i -- n>~rK\ - -\f\i~ tr i rMrfimn itrl

Greater than one (> 1) Left + 1

Smaller than one (< 1) Right - 1

The index of base 10 in a Standard Form helps us to recognise if a number isgreater or smaller than one:

Size of Number

Greater than one (> 1)

Smaller than one (< 1)

Index of Base 10

Positive

Negative

Example

4.2195 x 104 - 42195

5x1(T4 - 0.0005

Converting from Standard FormWhen expressing a number in Standard Form as ordinary notation we do the reverse:

Index of Base 10

Positive

Negative

Conversion of Standard Form to Number

Directional Shift of Decimal Point

Right

Result on Index ofBase 10 with each shift

- 1

Left + 1

Example 1:

Express in ordinary notation:

The diameter of Mars

= 6.8049 x106m

II) Distance travelled by light in one hour: 6.22x10 m

II!) Average width of a strand of human hair: 8x lO~ 5 m

Common SI Prefixes

10"

1012

109

10"

103

io-3

10"6

io-9

IO-12

Prefix

Tera

Giga

Mega

Kilo

M1U1

Micro

Nano

Pico

Symbol

T

G

M

K

m

M

n

P

Name

Trillion

Billion

Million

Thousand

Thousandth

Millionth

Billionth

Trillionth

Decimal

1 000 000 000 000

1 000 000 000

1 000 000

1 000

0.001

0.000001

0.000 000 001

0.000 000 000 001

METRIC PREFIX SCALE

T G Mtera, Mi

giga mega10' 10'

kkiloIO 3 10°

m jji(none) mil It micro nano pico

10 '6 1 ,-12

1 IO'1 ID"2

hecto deca deci centih da d c

Tip: How to remember

The Golden Monkey Kiss My Mama N^ Papa

Tera Giga Mega Kilo Mill! Micro Nano Pico

1 The speed of light is given as 3.00 * 108 m/s.(a) The distance from Sun to Venus is 1.08 x 10" m. How long does light take to travel from

the Sun to Venus? Express your answer in seconds.(b) If light takes 760 secondsto travel from the Sun to Mars, what is the distance from the Sun

to Mars? Express your answer in standard form.

2. The base area of a rectangle tank is 3 x 105 cm2 where its width and height are 4 x 102 cm and5 x 103 cm respectively. Showing your working clearly and leaving your answers in standard form,calculate(a) its volume,(b) its length.

3. The population of China in 2007 is approximately 1.30 x 109. The population of Thailand in 2007is approximately 6.50x10'.(a) Express the population of Thailand as a percentage of the population of China.(b) How many more people live in China than in Thailand in 2007? Leave your answer in

standard form.

4. One astronomical unit (AU) is equivalent to 150 gigametres.(a) Express 150 gigametres in metres, giving your answer in standard form.

(b) Given that the speed of light to be 3 x 108 mis, how many seconds does light take to travel1 AU?

5. The mass of a certain atom is 43 nanograms.(a) Write 43 nanograms in grams using standard form.(b) A container contains 4 billion atoms. Find the total mass in grams, of the atoms in the

container.

6. Given that a = 3 x l O and 6 = 9x10 , find the value of -- ^ , giving your answer in standard

a~V2

form.

Homework: PRACTICE IF

SCHOOL.. CLASS DATE.

NAME/INDEX NO... SUBJECT

IF

bOd;

£?• <?£><=> ^ C . X

723-4^ * T 2.34-5 o-A- = -4.

- /. O2

lo

-Jfl•y O-118

X

~ .46 X /o"J2-3 / 0s

y /o "q

.2-7

T 5 xo

i±j*= o

I5eis

SCHOOL. CLASS DATE _

NAME/INDEX NO. .. SUBJECT

£6%*^~

/O

•=- \o X /o

= i • ox I &£> x /O

h

133 -

. 33£

*)v to-*

n/>i

Vvrt/i A . S

\5o - 1-5 x

SCHOOL CLASS _ DATE _

NAME/INDEX NO SUBJECT

10£>&& &c?c> X

000 x/c?"'a

J) £L/o'4"

'X

0- 00 24-3 ^ P.&&2.4- - -?4-X/C>""

h x fo

- || 7 r

-4-f ^ /C?"'2- M ^ ||7

X

42 fk*- "fxA*-^- £^S»A <^s%r- r ( x

- -23 ;oX

3; x -- £-

f

tfeis

SCHOOL CLASS DATE _.

NAME/INDEX NO SUBJECT

=*-

3

£3P-

£- \o* \o~'~ n - f~" '"^

— /I ^y \O m ~ I • & X^ 't-X XV

11 IJ— - I / A- „» i ^> " I I * -w' -? - I V J /S* 't/\s> 'I C- t- /vii I) 6** - •" -^ i s^ I {/

= 4 X /C7 t f V 3- /

h

Vx

x~

y

I5eis

SCHOOL CLASS _ DATE _.

NAME/INDEX NO SUBJECT

lot) \OQ

x fo

ill-1-5 X 1C?'3