Scientific N

otation

Scientific N

otation

Scientific N

otation

Scientific N

otation

�Altern

ate way o

f writin

g numbers to

elim

inate u

nnecessary zero

s (usually u

sed

with

very large or very sm

all numbers).

�Scien

tific notatio

n m

ay be u

sed fo

r any number in

our calcu

lations.

number in

our calcu

lations.

�We will N

OT use scientific

notation

for:

◦temperature, m

oney, m

olecular m

asse

s, or p

H.

Scientific N

otatio

n

Scientific N

otatio

n

TW

O parts:

TW

O parts:

�Mantissa

/Coeffic

ient–is a (+

) or (-)

number >

-10 an

d < +10. (#

from 1 to

9.999)

◦7.00x 103­-the n

umber “7

.00” is th

e coefficien

t

�Characteristic

/Exponent–is a w

hole

Characteristic

/Exponent–is a w

hole

number ex

ponent th

at is the b

ase 10 is raised

.

◦8.75 x 104-the n

umber “4

” is the ch

aracteristic.

◦A (+

) characteristic m

eans th

at the n

umber is a

LARGEnumber

◦A (-) ch

aracteristic mean

s that th

e number is a

SMALLnumber

Form

:(# fro

m 1 to

9.999) x

10exponent/ch

aracteristic

800

= 8 x 10x 10

= 8 x 102

2531

= 2.531 x 10x 10x 10

2531

= 2.531 x 10x 10x 10

= 2.531 x 103

0.0014 =

1.4 / 1

0/ 1

0/ 1

0

= 1.4 x 10-3

Exam

ples

Exam

ples

convertin

g to scien

tific notatio

n (S.N

.):convertin

g to scien

tific notatio

n (S.N

.):

1.15400 1

.5400 x 104

2.0.00143

1.43 x 10-3

3.-78.5

-7.85 x 101

(Rem

ember ad

d th

e “-” back w

hen yo

u

complete co

nverting)

Change to

scientific n

otatio

n.

12,340 =

0.369 =

0.008 = 1

.234 x 104

3.69 x 10–1

8 x 10–3

0.008 =

1,000,000,000 =

8 x 10

1 x 109

Learn Check

Learn Check

1.Convert 2

24.50 to

S.N. _____________

2.Convert 0

.0034 to

S.N. _____________

3.Convert 5

.870 to

S.N. ______________

Expand

Expandscien

tific notatio

n to

scien

tific notatio

n to

regu

lar (or n

orm

al) notatio

nregu

lar (or n

orm

al) notatio

n

1.LOOK at th

e characteristic.

2.If th

e Characteristic is “+

” (i.e106) th

en

move th

e decim

al that m

any places in

the d

irection which

will m

ake the

the d

irection which

will m

ake the

norm

al number a large o

ne.

�Ex: 5

.6700 x 104

56700.0

�Ex: 8

.23 x

102

823

3.

LOOK at th

e characteristic/ex

ponent

4.

If the C

haracteristic/ex

ponent is “-” (i.e

10-6)

then m

ove th

e decim

al in th

e directio

n which

will

make th

e expanded number a sm

all (less than 1)

number

�Ex: 8

.45 x10-1

Expand

Expandscien

tific notatio

n to

scien

tific notatio

n to

regu

lar (or n

orm

al) notatio

nregu

lar (or n

orm

al) notatio

n

�Ex: 8

.45 x10-1

�8.45 x 10-1

0.845

�Ex: -6

.32 x 10-3

�-006.32 x 10-3

-0.00632

Change to

standard

form

.

1.87 x 10–5=

3.7 x 108=

370,000,000

0.0000187

000000187000000

..

3.7 x 10

=

7.88 x 101=

2.164 x 10–2= 3

70,000,000

78.8

0.02164

Learn Check

Learn Check

1.Expand 7.73 x 10-3_______________

2.Expand 4.32996 x 104_______________

3.Expand 3.2 x 100________________