1) Scientific notation is a way of writing numbers in the form c × 10n, where c is between 1 and 10 and n is an integer. 2) Scientific notation allows very large and very small numbers to be written easily without lots of zeros by moving the decimal point and changing the exponent. 3) Operations like multiplication and division with scientific notation follow the normal rules of exponents - the exponents are added or subtracted.

1. Algebra
8.4
Scientific Notation

2. The Form
A number is written in scientific notation
when it is in the form
n
c × 10
where c is a value ≥ 1and < 10
and n is an integer.

3. c × 10n
The
Form
where c is a value ≥ 1and < 10
and n is an integer.
Not Scientific Notation
31.2 × 10
.65 × 10
3
7
8042 × 10
−6
Scientific Notation
3.12 × 10
6.5 × 10
4
6
8.042 × 10
−3

4. Large and small values
One purpose of scientific notation is to allow
you to write very large numbers and very
small numbers easily, without lots of 0’s.
Large numbers have positive exponents.
84,912
8.4912 × 10
4
Small numbers have negative exponents.
.000265
2.65 × 10
-4

5. Scientific Notation
Decimal
Move decimal point right for positive exponent.
Move decimal point left for negative exponent.
1.
3.128 × 10
2.
6.4 × 10
3.
3.9 × 10-1
.39
4.
6.12 × 10-5
.0000612
3
4
3128
64,000

6. Decimal
Scientific Notation
Move decimal point right or left to arrange one
digit to the left of decimal point.
1.
52,314
Move left 4 places
2.
3.2
5.2314 × 10
No need to move
3.
4.
.0000428
Move right 5 places
602,000,000
Move left 8 places
4
3.2 × 10 0
4.28 × 10-5
6.02 × 10
8

7. Exercises
Rewrite in decimal form.
1.
2.834 × 10
2.
1.23 × 10
2
-6
283.4
.00000123
Rewrite in scientific notation.
3.
4.
34,690
3.469 × 10
.039
3.9 × 10
-2
4

8. Computing with Scientific Notation
Another purpose of scientific notation is to
allow you to compute with large and small
values easily using the rules of exponents.
Numbers can be multiplied.
(8 × 10 ) (3 × 10 )
4
2
= (8 × 3) (10 × 10 )
4
= 24 × 10
4+2
2
= 24 × 10 = 2.4× 10
6
7

9. Computing with Scientific Notation
Numbers can be divided.
4.8 × 10
4.8 10
=
×
2
2
2.4 × 10
2.4 10
6
= 2 × 10
6-2
6
= 2 × 10
4

10. Exercise
Evaluate. Write answer in scientific notation.
(1.4 × 10 ) (7.6 × 10 )
4
3
= (1.4 × 7.6) (10 × 10 )
4
3
10.64 × 10
7
1.064 × 10
8
Associative property
Simplify
Rewrite in SN

11. Exercise
Evaluate. Write answer in scientific notation.
(8 × 10 )
-5
(5 × 10 )
-3
 8   10 
= ÷  -5 ÷
 5   10 
-3
1.6 × 10
-3-(-5)
1.6 × 10
2
Associative property
Subtract exponents
Simplify to SN

12. Homework
pg. 63 #’s 1, 2, 4, 6, 8, 9, 10, 11