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Scientific Notation
Scientific Notation
At the conclusion of our time
together, you should be able to:
1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard
number
What is Scientific Notation?
 Scientific notation is a way of expressing really big
numbers or really small numbers.
 For very large and very small numbers, scientific
notation is more concise.
Scientific Notation Consists Of Two Parts:
 M = A number between 1 and 10
 n = A power of 10
n
M x 10
Scientific Notation
n
M x 10
 M is the coefficient 1<M<10
 10 is the base
 n is the exponent or power of 10
Other Examples:
5.45E+6
5.45 x 10^6
Numbers Less Than 1 Will Have A Negative
Exponent.
A millionth of a second is:
0.000 001 sec
1.0E-6 s
1 x 10-6 s
1.0 x 10^-6 s
To Change Standard Form To Scientific
Notation…
 Place the decimal point so that there is one non-
zero digit to the left of the decimal point.
 Count the number of decimal places the decimal
point has “moved” from the original number. This
will be the exponent on the 10.
 If the original number was less than 1, then the
exponent is negative. If the original number was
greater than 1, then the exponent is positive.
Examples




Given:
289 800 000 m
Use:
2.898 m (moved 8 places)
Answer: 2.898 x 108 m
Easier Way = M term smaller, so make
n term larger - 100 to 108




Given:
0.000 567 m
Use:
5.67 m (moved 4 places)
Answer: 5.67 x 10-4 m
Easier Way = M term larger, so make
n term smaller - 100 to 10-4
To Change Scientific Notation To Standard
Form…
 Simply move the decimal point to the right for
positive exponent of 10.
 Move the decimal point to the left for negative
exponent of 10.
(Use zeros to fill in places.)
Example
 Given:





5.093 x 106 m
Answer: 5 093 000 m (moved 6 places to
the right)
Easier Way = 106 to 100 = n smaller, so make
M term larger!
Given:
1.976 x 10-4 m
Answer: 0.000 197 6 m (moved 4 places to the
left)
Easier Way = 10-4 to 100 = n larger, so make
M term smaller!
Scientific Notation
Let’s see if you can:
1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard
number
Learning Check
 Express these numbers in Scientific
Notation:
1)
2)
3)
4)
5)
405 000 cm
0.003 872 cm
3 000 000 000 cm
2 cm
0.478000 cm
4.05 x 105 cm
3.872 x 10-3 cm
3 x 109 cm
2 x 100 cm
4.78000 x 10-1 cm
Scientific Notation
Calculations
Scientific Notation
At the conclusion of our time
together, you should be able to:
1. Multiply and divide numbers that are in
scientific notation
2. Add and subtract numbers that are in
scientific notation
Example #16
 (3 x 102 m)(8 x 10-4 m)
 Answer: multiply M terms
24
 Add n terms

-2

24 x 10-2 m2
 Adjust to correct scientific notation

2.4 x 10-1 m2
 Adjust to correct number of sig figs

2 x 10-1 m2

Example #17
 (5.000 x 105 m)/(3500 m)
 Answer: divide M terms
0.001 428
 Subtract n terms

5

0.001 428 x 105
 Adjust to correct scientific notation

1.428 x 102
 Adjust to correct number of sig figs

1.4 x 102

Example #18
 (5.0 x 104 m)(8.230 x 106 m)
/(1.99 x 1018 m)
 Answer: multiply and divide M terms

20.678 m
 Add and subtract n terms

-8

20.678 x 10-8 m
 Adjust to correct scientific notation

2.0678 x 10-7 m
 Adjust to correct number of sig figs

2.1 x 10-7 m
Example #13
 (5.0 x 10-3 m)-(5.0 x 10-8 m)
 Answer: can only subtract like powers
 Adjust to larger power
 (5.0 x 10-3 m)-(0.000050 x 10-3 m) =
4.999950 x 10-3 m
 Adjust to correct number of decimal places

5.0 x 10-3 m
 Adjust to correct scientific notation

5.0 x 10-3 m

Example #14
 (5.0 x 10-3 m) + 0.774 m
 Answer: can only add like powers
 Adjust to larger power
 (0.0050 x 100 m) + 0.774 m =
0.7790 m
 Adjust to correct number of decimal places

0.779 m
 Adjust to correct scientific notation

7.79 x 10-1 m

Example #15
 (5.0 x 10-3 m) + (5.0 x 10-4 m) - 0.009 38 m
 Answer: can only add like powers
 Adjust to larger power
 (0.0050 x 100 m) + (0.000 50 m) – 0.009 38 m
-0.003 88 m
 Adjust to correct number of decimal places

-0.003 9 m
 Adjust to correct scientific notation

-3.9 x 10-3 m

Scientific Notation
Let’s see if you can:
1. Multiply and divide numbers that are in
scientific notation
2. Add and subtract numbers that are in
scientific notation