ctur*
Date
Operations with Scientific
Use
-
with Appendh
B,
Operations with
Scientilic Notation
Notation
5A
5f
Operations with Scientific
Notation
Uie with Appendh
B,
operationi wfth
Scientlfi. ilot.tion
1. Peribrm the following opcrations md oxprcss the mswen itr scientific notation.
Addition and Subtractlon
..
(1.2
b.
(6.91
x
to-2) + (2.4
c.
(9.70
x
106) + (8.3
x ld)
d.
(3.67
x
ro2)
-
x lol)
x
105)
x
+ (5.35
105)
Before numbers in scientific notation can be added or
subtracted, the exponents must be equal.
(3.4
x
[102)
*",
"0r",
+ (4.57 x
I
103)
+
-
The decimal is moved
to the left to increase
the exponent.
++
r-
= (0.34 x
103)
Equal
+
(4-57
---r
x't03)
__J
-
(0.34 + 4.57)
= 4.91
x
x
103
(1.6
x
1o-3)
103
e. (8.4t
x lo-s)
f.
x rd) -
(7.9
x r0-9
Multiplication
When numbers in scientific notation are multiplied. only the
number is multiplied. The exponents are added.
(r.33
(+.q
x rd)
!
3
.ii
(2.00
B
x
1gr)(4.00
x
rt
10a)
=
;
q
5
= (2.00x4.00) x
= 8,00
x
Pertbm the following opeations md exprcss the answers in scientilic notation
103+4
107
a,
(4.3
x
108)
x
(2.0
x
b.
(6.0
x
16:y
x
1r,5
x lo-2)
c.
(1.5 X 10-2)
H'
106)
d
2
I
E
d
E
z
6
d
x
(8,0
x 10-l)
.9
r
Dfuision
When numbers in scientific notation are divided, only the
number is divided, The exponents are subtracted.
ffi.
1'60 x
10i_
':l'0
= 5.00
Math Handbook Tran!parency Masterg
d.
7.8
x
g
to3
z
i
r2;lF'
8.1
x
E
6
lo-2
l"illot
__J
x
(il
103
Chemirtry: Matter and Change
6.48
t
x ld
xl6(t-8 x 10-
Ch€mistry: Matter and
change
Math Hahdbook Trahsparency Worksheet!
Ddc-
J4
|5il
clas
Scientific Notation
L
a.
Scientists need to express small measurements, such as the
mass of the proton at the center of a hydrogen atom
(0.000 000 000 000 000 000 000 000 001 673 kg), and large
measurements, such as the temperature at the center of
the Sun (1 5 000 000 K). To do this conveniently, they
express the numerical values of small and large
measurements in scienti{ic notation, which has two parts.
fo*il;il]
I ;il:;,tt':':1,
l---- N x
of ttre oecimal
i
|
----] ;lJ:iIilJi
mukiplied
|
Thus, the temperature of the Sun, 15 million kelvins,
written as 1.5 x 107 K in scientific notation.
E
Each.time
decimal
place is
moved one
place to the
left,
the
E
E
,2
B,
numbers iD scientitic notation
230
C.
14 100
d.
56
ffx)
million
e,
I
I
f.
0.450 t3
g.
0.089
is
h. 0.000 26
Positive Exponents
&
followilg
with Appendir
Scaentiti. I{otation
b.5601
f **-***_l
10n
Express each of the
Use
Express 1234.56 in scientific notation.
12?4.56
!
i. 0.000 000 698
x 100 = 123,456 x 101
121456 x 101 = 12.3456 x 102
12,3456 x 102 = 1.234 56 x lo3
v
'1.234 56 x 103
1234,56
v
g
the
exponent
6
is
i.
increased by
12 rhousandth
a
one'
2,
!
Express each of the tbtlowing measurements in scientitrc notation.
a,
speed
b.
number oI seconds in a day, 86 400
c.
mear radius ofEuth.6378 knl
d.
density of oxygen gas at OoC and pressure
e.
radius of an argon atom, 0.000 000 000 098 m
of light in a vacuum, 299 792 458 rn/s
;
e
Negative Exponentt
s
9
2
Express 0.006 57 in scientific notation.
!
.8
'E.
Each
5
the
time
decimal
place is
moved one
place to the
right,
0.006 57
= 0.0657 x 10-1
0.0557 x 10-1 = 0.657 x 10-2
11 10-2 = 6.57 x 10-3
OISZ
\./
0.006 57
v
6.57
Math Handbook Tranlparency Maitets
x
x
100
the
exponent
is
decreased
by one.
of
101 kPa, 0,001 42 g/ml-
10-3
Chemistry: Matter and Change
Chemistry: Matter and Change
Math Handbook Transparency Worksheets
I
d