PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
Review:
Scientific notation expresses a
number in the form:
M x
1  M  10
n
10
n is an
integer
6
10
4 x
6
+ _______________
3 x 10
7 x 106
IF the exponents are
the same, we simply
add or subtract the
numbers in front and
bring the exponent
down unchanged.
6
10
4 x
6
+ _______________
3 x 10
7 x 106
IF the exponents are
the same, we simply
add or subtract the
numbers in front and
bring the exponent
down unchanged.
106
4 x
+ 3 x 105
If the exponents are
NOT the same, we
must move a decimal
to make them the
same.
6
10
4.00 x
4.00 x
6
5
+ .30 x 10
+ 3.00 x 10
6
4.30 x 10
Move the
decimal on
the smaller
number!
6
10
A Problem for you…
-6
10
2.37 x
-4
+ 3.48 x 10
Solution…
-6
002.37
2.37 x 10
-4
+ 3.48 x 10
Solution…
-4
0.0237 x 10
-4
+ 3.48
x 10
-4
3.5037 x 10
2.0 x
102
+ 3.0 x
103
.2 x 103 + 3.0 x 103
= .2+3 x 103
= 3.2 x 103
Addition and subtraction
Scientific Notation
1. Make exponents of 10 the same
2. Add 0.2 + 3 and keep the 103 intact
The key to adding or subtracting numbers
in Scientific Notation is to make sure the
exponents are the same.
2.0 x 107 - 6.3 x 105
2.0 x 107 -.063 x 107
= 2.0-.063 x 107
= 1.937 x 107
1. Make exponents of 10 the same
2. Subtract 2.0 - .063 and
keep the 107 intact
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
MULTIPLYING AND DIVIDING
Rule for Multiplication
When multiplying with scientific notation:
1.Multiply the coefficients together.
2.Add the exponents.
3.The base will remain 10.
(2 x 103) • (3 x 105) =
6 x 108
(9.2
x 105) x (2.3 x 107) =
21.16 x 1012 =
2.116 x 1013
(3.2 x 10-5) x (1.5 x 10-3) =
4.8 • 10-8
Rule for Division
When dividing with scientific notation
1.Divide the coefficients
2.Subtract the exponents.
3.The base will remain 10.
6.20 x 10 – 5
8.0 x 10 3
6.20
8.0
= 0.775 x 10
10 -5
10
3
DIVIDE USING SCIENTIFIC
NOTATION
1.
Divide the # ’s &
Divide the powers of ten
(subtract the exponents)
2.
Put Answer in Scientific
Notation
-8
= 7.75 x 10 – 9
(8 • 106) ÷ (2 • 103) =
4 x 103
(3.402 x 105) ÷ (6.3 x 107) =
0.54 x 10-2
Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) =
(3 x 105) x (7 x 104) =
(5.63 x 108) x (2 x 100) =
(4.55 x 10-14) x (3.77 x 1011) =
(8.2 x10-6) x (9.4 x 10-3) =
Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) = 2.62 x 10-1
(3 x 105) x (7 x 104) = 2.1 x 1010
(5.63 x 108) x (2 x 100) = 1.13 x 109
(4.55 x 10-14) x (3.77 x 1011) = 1.72 x 10-2
(8.2 x10-6) x (9.4 x 10-3) = 7.71 x 10-8
Please divide the following numbers.
1. (5.76 x 102) / (4.55 x 10-4) =
2. (3 x 105) / (7 x 104) =
3. (5.63 x 108) / (2) =
4. (8.2 x 10-6) / (9.4 x 10-3) =
5. (4.55 x 10-14) / (3.77 x 1011) =
Please divide the following numbers.
1. (5.76 x 102) / (4.55 x 10-4) = 1.27 x 106
2. (3 x 105) / (7 x 104) = 4.3 x 100 = 4.3
3. (5.63 x 108) / (2 x 100) = 2.82 x 108
4. (8.2 x 10-6) / (9.4 x 10-3) = 8.7 x 10-4
5. (4.55 x 10-14) / (3.77 x 1011) = 1.2 x 10-25
Changing from Standard
Notation to Scientific Notation
Ex. 6800
1. Move decimal to get
a single digit # and
count places moved
6800
3
2
1
3
68 x 10
Ex. 4.5 x 10
00045
2. Answer is a single
digit number times
the power of ten of
places moved.
3
2
1
-3
Changing from Scientific
Notation to Standard Notation
1. Move decimal the same
number of places as the
exponent of 10.
(Right if Pos. Left if
Neg .)
9.54x107 miles
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.
1.86x107 miles
per second
What is Scientific Notation
Multiply two numbers
in Scientific Notation
(3 x 10 4 )(7 x 10 –5 )
4
= (3 x 7)(10
x 10 –5 )
1.
= 21 x 10 -1
= 2.1 x 10
2.
3.
4.
0
or 2.1
6.20 x 10 – 5
8.0 x 10 3
6.20
10 -5
8.0
10 3
= 0.775 x 10
Put # ’s in ( ) ’s Put
base 10 ’s in ( ) ’s
Multiply numbers
Add exponents of 10.
Move decimal to put
Answer in Scientific
Notation
3
or
2.0 x 10
2
Why do we use it?
It’s a shorthand way of writing very large or very
small numbers used in science and math and
anywhere we have to work with very large or very
small numbers.
DIVIDE USING SCIENTIFIC
NOTATION
.2 x 10
3
+ 3.0 x 10
+ 3.0 x 10
= 3.2 x 10
1.
2.
Divide the # ’s &
Divide the powers of ten
(subtract the exponents)
Put Answer in Scientific
Notation
7
2.0 x 10
2.0 x 10
7
3
Addition and subtraction
Scientific Notation
1. Make exponents of 10 the same
2. Add 0.2 + 3 and keep the 10
3
intact
The key to adding or subtracting numbers
in Scientific Notation is to make sure the
exponents are the same.
3
- 6.3 x 10
-.063 x 10
= 2.0-.063 x 10
= 1.937 x 10
3
3
= .2+3 x 10
-8
= 7.75 x 10 – 9
A number expressed in scientific notation is
expressed as a decimal number between 1 and 10
multiplied by a power of 10 (
eg , 7000 = 7 x 10
-6
0.0000019 = 1.9 x 10
)
Scientific
Notation
Makes
These
Numbers
Easy
7
7
5
7
1. Make exponents of 10 the same
2. Subtract 2.0 - .063 and
keep the 10 7 intact