1. Scientific Notation

2. Why use scientific notation:
Consider the equation:
Find the force between an electron and the Earth when the electron is on the surface of the earth

3.  with only 1 digit to the left of the decimal point Left - Larger
Scientific Notation
Writing numbers using powers of ten
with only 1 digit
to the left of the
decimal point 4
35 000
3.5 x 10 -3
4.67
x 10
Changing numbers to scientific notation
Move the decimal pt. to the left-
make the exponent larger for each step
Left - Larger
Move the decimal pt. to the right-
make the exponent smaller for each step 
exponent
decimal
Right - Reduce

4. Move decimal 4 places to the left to reach 3.5, add 4 to the exponent
35 000
3.5 x 104
Same as
x 100
Move decimal 4 places to the left to reach 3.5,
add 4 to the exponent
(Left – Larger)
Same as
4.67 x 10-3
x 100
Move decimal 3 places to the right,
subtract 3 from the exponent
(Right Reduce)

5. To expand a number from scientific notation with a positive exp:
reduce the exponent to zero and move the decimal point to the right for each reduction of 1.
(Reduce Right)
5.635 x 105 =
If the exp. is negative, increase the exp. to 0, and
move the exponent left for each 1 added.
4.879 x =
(Larger – Left)

6. Numbers should be expressed in proper notation
Proper Notation - Only 1 number to the left of the decimal in the coefficient
Express the following in proper notation
359.4 x 104 = x 10?
3.594 x 106
0.468 x 10-6 =4.68 x 10?
4.68 x 10-7
358 x 105 = ?
3.58 x 107
0.020 x 104 = ?
2.0 x 102
(Left – Larger)
(Right Reduce)

7. Multiplication / Division Rules
Mathematical Operations with Scientific Notation
Multiplication / Division Rules
1. Multiply the coefficients
2. Add the exponents
3. Place in Proper Notation
1. Divide the coefficients
2. Subtract the exponents
3. Place in Proper Notation
6) x 107
3.0 x 10-3
5) x 104
x 3.0 x 10-6
add
subtract
(4 +(-6))
= -2
(7 -(-3))
= 10
15.0 x 10-2
3.0 x 1010
1.5 x 10-1

8. Keep same exponent Written in proper form
Addition and Subtraction Rules with Sci not
1. Make exponents the same, if not already
2. Add or Subtract coefficients
3. Keep the same exponent
4. Change to Proper Notation ( if not already)
Examples
1) x 105
+8.2 x 105
Exponents are already the same
Keep same exponent
13.8 x 105 6
Written in proper form
1.38 x 10

9. Addition and Subtraction Rules with Sci not
2) x 10-3
+ 3.4 x 10-4
Need to match exponents
4.5 x 10-3
Keep value with higher exp the same
Change lesser valued exp to match higher
and adjust coefficient +
0.34
x 10-3
4.84 x 10-3
Already in correct form
x 105
- 4.8 x 107
x 105
- 4.8 x 104
0.069
x 107
6.9 x 105
x 107
-0.48
x 105
x 107
6.42 x 105