PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
Review:
Scientific notation expresses a
number in the form:
M x
Any number
between 1
and 10
n
10
n is an
integer
Solution…
-4
0.0237 x 10
-4
+ 3.48
x 10
-4
3.5037 x 10
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
(4.6x108) (5.8x106) =26.68x1014
Notice: What is wrong with this example?
Although the answer is correct, the
number is not in scientific notation.
To finish the problem, move the decimal one
space left and increase the exponent by
one.
26.68x1014 = 2.668x1015
((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.
(8 • 106) ÷ (2 • 103) =
4 x 103
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
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
Raising Numbers in Scientific
Notation To A Power
(5 X 104)2 =
(5 X 104) X (5 X 104) =
(5 X 5) X (104 X 104) =
(25) X 108 = 2.5 X 109
Try These:
1. (3.45 X
1010)2
1.19 X 1021
2. (4 X 10-5)2
1.6 X 10-9
3. (9.81 X 1021)2
9.624 X 1043
1. (3.45 X 1010)2 = (3.45 X 3.45) X (1010 X 1010) = (11.9) X
(1020) = 1.19 X 1021
2. (4 X 10-5)2 = (4 X 4) X (10-5 X 10-5) = (16) X (10-10) = 1.6 X
10-9
3. (9.81 X 1021)2 = (9.81 X 9.81) X (1021 X 1021) = (96.24) X
(1042) =
9.624 X 1043