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Scientific Notation
why it’s used, when to use it,
review of standard sci. notation
Why sci. not.?
The #s for scien. msmnts are often very
large or very small
Earth to the Moon is 384,403,000 m
E. coli, is .0000011 to .0000015 m wide
Standard Scientific Notation
Which one is in std. sci.not.?
0.486 x 10-3 km 2.50 x 101 ºC
904.6 x 10-2 g
Std. sci.not.: a number between 1 to 9, followed by
a decimal point and more digits, then “ x 10 to a
power”
Power can be negative or positive
+/- powers, and moving the decimal
Expanding:
Putting in std. sci.not:
How to use “EE” notation in your
calculator and practice problems
Scientific Notation
Well now what, how do I do all the
operations?
Addition and Subtraction
• Change the #s so that all exp. are the same.
• Add or subtract coefficients
• Put in std. sci.not.
(2.0 x 103) + (3.0 x 102) =
(2.0 x 103) + (0.3 x 103) =
(2.0 + 0.3) x 103 =
2.3 x 103
Now you try it!
(2.35 x 107 g) – (6.32 x 105 g)
(4.80 x 108 g) – (1.3 x 103 g)
Multiplication
• Add the exponents on the 10s together
• Multiply the coefficients
• Put it together, and put answer in std. sci.
not.
(4.0 x 105) x (3.0 x 10-1)
105 x 10-1 = 10(5-1) = 104
( 4.0 x 3.0) x 104 = 12 x 104
1.2 x 103
Now you try!
(8.0 x 108 cm) x (6.0 x 102 cm) =
(4.78 x 105 cm) x (8.9 x 107 cm) =
Division
• Divide the coefficients first, put result in numerator
• Move power of ten in denominator to numerator,
switching the sign on the exponent. It’s now a
multiplication problem.
• Add the exponents
• Put it together and put in std. sci. not.
6.0 x 108 = 2.0 x 108 = 2.0 x 108 x 10-5 = 2.0 x 103
3.0 x 105 1.0 x 105
2.0 x 103
Now you try it!
(3.6 x 108 g) =
(1.2 x 104 mL)
(1.02 x 103 g) =
(3.60 x 107 mL)
Sci. Not. HW