OB: Scientific Notation for fun
and personal enjoyment
You must start with a calculator in hand.
Do the math in the proper order and
you’ll always be right!
Homework tonight, #4, Scientific Notation
Express the following as Scientific Notation:
17,000,000,000 ants _________________________
6,374,000 meters _________________________
0.034 gram _________________________
0.000 000 000 154 meters (the radius of a carbon atom _________________________
0.000 008 m (the diameter of a human hair) _________________________
Express the following as Scientific Notation:
17,000,000,000 ants 1.7 x 1010 ants
6,374,000 meters 6.374 x 106 m
0.034 gram 3.4 x 10-2 g
0.000 000 000 154 meters (the radius of a carbon atom 1.54 x 10-10 m
0.000 008 m (the diameter of a human hair) 8 x 10-6 m
Chem scientific notation rule: the coefficient shall always be more than one, less than ten
For example, THESE ARE ALL EQUAL, BUT…
60,500 = 605 x 102
60,500 = 60.5 x 103
60,500 = 6.05 x 104
60,500 = 0.605 x 105
But in our class only the red answer is acceptable.
Problem 1
Convert 36.8 kilograms into ounces,
answer to be given in scientific notation.
(hints: 454 g = 1 pound = 16 ounces) (1kg = 1000 grams)
Round to correct SF.
Problem 1
Convert 36.8 kilograms into ounces, answer to be given in scientific notation.
(hints: 454 g = 1 pound = 16 ounces)
36.8 kg
x
1
1000 g x
1 kg
1p
454 g
x 16 oz
1p
=
588 800
= 1296.9163 oz
454
1.30 x 103 oz
Problem 2
Convert 300. seconds into years,
answer as scientific notation
(hint: your answer will be a small fraction of years, your exponent must be negative)
Problem 2
Convert 300. seconds into years, answer as scientific notation
(hint: your answer will be a small fraction of years, your exponent must be negative)
300. sec
x
1
1 min x 1 HR x 1 day
1 year
x
=
60 sec
60 min
24 HR
365 day
30.0
31536000
= 0.00000950 years = 9.50 x 10-6 years
Multiplication rules for scientific notation
Multiply coefficients, add powers of ten, adjust coefficient if necessary. (teapot)
(3 x 105)(2 x 102) =
5.0 x 104
X 3.0 x 102
Multiplication rules for scientific notation
Multiply coefficients, add powers of ten, adjust coefficient if necessary. (teapot)
(3 x 105)(2 x 102) = 6 x 107
5.0 x 104
X 3.0 x 102
1.50 x 107
15.0 x 106
1.5 x
7
10
with 2 SF
Division Rules for Scientific Notation
Divide coefficients, subtract powers of ten, adjust coefficients (teapot) if necessary.
3.0 x 104
2.0 x 102
9.0 x 105
=
3
3.0 x 10
=
Division Rules for Scientific Notation
Divide coefficients, subtract powers of ten, adjust coefficients (teapot) if necessary.
3.0 x 104
2.0 x 102
= 3.0 X 10(4-2) = 1.5 x 102
2.0
9.0 x 105 = 9.0
(5-3)
2
X
10
=
3.0
x
10
3
3.0 x 10
3.0
Addition and Subtraction rules:
Adjust scientific notation so both terms have the SAME POWERS OF TEN, add or subtract
coefficients, then adjust answer if necessary (teapot)
6.5 x 107
+ 2.2 x 107
6.2 x 108
+ 1.5 x 106
Addition and Subtraction rules:
Adjust scientific notation so both terms have the SAME POWERS OF TEN, add or subtract
coefficients, then adjust answer if necessary (teapot)
6.5 x 107
+ 2.2 x 107
8.7 x 107
6.2 x 108
+ 1.5 x 106
6.2 x 108
+ 0.015 x 108
6.215 x 108
6.2 x 108
Addition and Subtraction rules:
Adjust scientific notation so both terms have the SAME POWERS OF TEN, add or subtract
coefficients, then adjust answer if necessary (teapot)
8.5 x 103
- 2.4 x 103
7.1 x 105
- 1.6 x 104
Addition and Subtraction rules:
Adjust scientific notation so both terms have the SAME POWERS OF TEN, add or subtract
coefficients, then adjust answer if necessary (teapot)
8.5 x 103
- 2.4 x 103
6.1 x 103
7.1 x 105
- 1.6 x 104
7.1 x 105
- 0.16 x 105
6.94 x 105
6.9 x 105
8.72 x 1011
+ 1.72 x 1010
4.65 x 1014
- 2.25 x 1015
8.72 x 1011
+ 1.72 x 1010
8.72 x 1011
+ 0.172 x 1011
8.892 x 1011
8.89 x 1011
4.65 x 1014
- 2.25 x 1015
0.465 x 1015
-2.25 x 1015
-1.785 x 1015
-1.79 x 1015
6.02 x 1023
x 1.50 x 102
(9.05 x 1019) ÷ (3.2 x 1016 ) =
6.02 x 1023
x 1.50 x 102
9.03 x 1025
(9.05 x 1019) ÷ (3.2 x 1016 ) = 2.8 x 103