Download Scientific Notation

Integrated Algebra
NOTES: Scientific Notation
Name
Let’s review !!
Scientific Notation is a short cut for writing very large or very small numbers.
Scientific notation is the product of two factors: a decimal greater than or
equal to 1 and less than 10: 1 ≤ d < 10 (basically there can only be one nonzero number in front of the decimal place) AND an integer power of 10.
ex)
2.3 x 104
1.003 x 108
3 x 10-3
4.124 x 10-5
To write a number greater than 10 in Scientific Notation:
- move the decimal point until there is only one non-zero number to
the left of it
- count how many places you moved the decimal point to the left
- write the number of places the decimal moved as the exponent
ex) 34,510,000. = 3.451 x 107
To write a number between 0 and 1 in Scientific Notation:
- move the decimal point until there is only one non-zero number to
the left of it
- count how many places you moved the decimal point to the right
- write the negative of the number of places the decimal moved as the
exponent
ex) .000357 = 3.57 x 10-4
To write a number from Scientific Notation to Standard form:
- move the decimal place according to the exponent
(a) if negative move it that many places to the left
(b) if it is positive move it that many places to the right
ex)
5.6 x 104 = 56,000
1.78 x 10-4 = .000178
Integrated Algebra
More Review………..
When multiplying powers with the same base, keep the base add the
exponents.
When dividing powers with the same base, keep the base subtract the
exponents.
ex)

104 x 102 = 106
10-3 x 1012 = 109
10 7
= 102
10 5
105
10 9
Try: 106 x 10-4
= 10-14
10-8 x 10-2

107
102
10 3
105
Now that we’ve reviewed, we should be ready to multiply and divide in
 scientific notation.

Multiplying Numbers in Scientific Notation
310 4 10  = 3 4  10
3
5
= 12 x 108

Try:
(2 x

x 109)
10-6)(5
3
105  Regroup (associative property) and
use the rules for multiplying
(6 x 10)(4 x 1012)
Let’s see: (3.23 x 103)(3.4 x104) Write answer in scientific notation.
3.23 3.4  103 104 10.982 107 not in scientific notation

10.982 x 107 need to move decimal one more place to the left
so need to add another power of ten
1.0982 x 108
Integrated Algebra
Dividing Numbers in Scientific Notation
2.8 10 
1.4 10 
6
3
2.8  10 
1.4  10 3 
6
=
Regroup and use rules for dividing each
2 10 3


Try:

3 10 
1.5 10 
4.6 10 
2.5 10 
8
7
2
2


**Don’t forget that if the product or quotient doesn’t end up in scientific
notation, then you may need to put it in scientific notation. Read the
directions and questions carefully to determine exactly how the question is
to be answered.
**Graphing Calculator**
The Graphing Calculator can be used to put standard numbers into scientific
notation and also scientific notation to standard form. Multiplication and
Division can also be done with the Graphing Calculator. This is a great tool to
check your answers. Remember if a scientific notation question is presented in
a part II, III, or IV question on the regents, then your work must be shown.
http://mathbits.com/mathbits/TISection/General/ScientificNotation.htm
Integrated Algebra
HOMEWORK: Scientific Notation
Name
Write each number in Scientific Notation.
1) 34,500,000
2) 5,004
3) .034
4) .0000056
5) .345 x 106
Write each number in Standard Form.
6) 6.34 x 106
7) 4.002 x 10-5
8) 1.9 x 10-4
9) 5 x 102
Write product or quotient in Scientific Notation.
10) 2 10

3
4 10 
3.58 10 
2 10 
4
12)

2
11)
4.2 10 
1.5 10 
13)
6.2 10 1.8 10 
8
6

3
4
3

14) The human eye blinks about 6.25 x 106 times each year. A 15 year old
would have blinked how many times? Write your answer in Scientific
Notation.
15) A single-celled organism is about 2 x 10-3 inches long. How many of these
organisms would have to be lined up to make a foot?