two parts: scientific...
TRANSCRIPT
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________________