1. Scientific Notation- Why?
Also used to maintain the correct number of significant figures.
An alternative way of writing numbers that are very large or very small.
characteristic will be positive
Ex: 6.022X1023

2. 6.02 x 1023 Method to express really big or small numbers.
Format is Mantissa x Base Power
Decimal part of
original number
Decimal
you moved
6.02 x 1023
Characteristic
We just move the decimal point around.

3. Using the Exponent Key on a Calculator

4. EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023:
How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2
Don’t do it like this…
WRONG! 6
y x . 3 2
WRONG!
…or like this… x 1 6 . 2 EE 3
…or like this:
TOO MUCH WORK.
y x 3 2 x 1 6 .

5. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
–09
Calculator gives…
E–09
or…
This is NOT written…
4.3–9
4.3 x 10–9
4.3 E –9 or
But instead is written…

6. Converting Numbers to Scientific Notation
2.205 x 10-5 1 2 3 4 5
In scientific notation, a number is separated into two parts.
The first part is a number between 1 and 10.
The second part is a power of ten.

7. Scientific Notation- How
To convert TO scientific notation,
move decimal to left or right until you have a number between 1 & 10.
Count # of decimal places moved
If original is smaller than 1 than characteristic will be negative
If original is larger than 1 the
If original number is negative, don’t forget to put the – back on the front!

8. Convert 159.0 to scientific notation Convert -0.00634
Example:
If you move the decimal to the left the characteristic will be positive
If you move the decimal to the right the characteristic will be negative
Convert to scientific notation
1.59 x 102
Convert
-6.34 x 10-3

9. Your Turn
10.2
-67.30
4.76
301.0
1.76 x 104
1.35 x 10-3
1.02 x 101
x 101
4.76 x 100
x 10-1
3.010 x 102
-1.30 x 10-4
May drop leading zeros - keep trailing

10. Expand Scientific Notation
If characteristic is positive move decimal to the right
If the characteristic is negative move the decimal to the left
Ex: 8.02 x 10-4
-9.77 x 105
-977,000

11. = x 10-9
report -6.5 x 10-9 (2 sig. figs.)
= x 103 or
report 5.35 x 103 (3 sig. figs.)
= x 10-13
report 5.84 x (3 sig. figs.)
= x 1023
report 2.9 x 1023 (2 sig. figs.)
= x 1016
report -3.1 x 1016 (2 sig. figs.)

12. Correcting Scientific Notation
The mantissa needs to have one place holder to the left of the decimal (3.67 not 36.7), look at the absolute value
Count how many decimals places you move and then you will increase or decrease the characteristic accordingly
If you must INCREASE the mantissa, DECREASE the characteristic
If you must DECREASE the mantissa, INCREASE the characteristic
Be careful with negative characteristics!
If you decrease 10-3 by two the new value is 10-5

13. Confused? Example To correct 955 x 108 -9445.3 x 10-6
Convert 955 to 9.55 – (move decimal left 2 times).
Did we increase or decrease 955?
955 is larger than 9.55 so we decreased it -so we must increase 8 by 2.
955 x 108 becomes 9.55 x 1010
x 10-6
Convert to (move decimal left 3 times).
Did we increase or decrease ? (absolute value)
We decreased the absolute value by 3 decimal places, so we must increase the characteristic

14. Your Turn
36.7 x 101
x 103
75.4 x 10-1
-14.5 x 102
0.123 x 104
97723 x 10-2
851.6 x 10-3
94.2 x 10-4
x 103
966 x 10-1
3.76 x 102
-1.5 x 10-5
7.54 x 100
-1.45 x 103
1.23 x 103
x 102
8.516 x 10-3
9.42 x 10-4
-1.2 x 101
9.66 x 10-1
May drop leading zeros - keep trailing

15. Rule for Multiplication Calculating with Numbers Written in Scientific Notation
MULTIPLY the mantissas
Algebraically ADD the characteristics
Correct the result to proper scientific notation when needed
Sample Problem: (4 x 10-3) (3 x 10-3)
(4) x (3) = 12
1.2 x 102
(-3) + (4) = 1 or 101

16. Rule for Division Calculating with Numbers Written in Scientific Notation
DIVIDE the mantissas
SUBTRACT the characteristic of the denominator from the characteristic of the numerator
Correct the result to proper sci. notation if needed
Sample Problem: Divide 7.2 x by -8 x 105 .
(7.2) (-8) = -0.9 .
-0.9 x 10-9
(-4) - 5) = -1 or 10-9
Correct: -9 x 10-10

17. Your Turn (2 x 104)(3 x 10-3) (5 x 10-3)(4 x 10-4) (6 x104)(-7 x 10-5)
May drop leading zeros - keep trailing

18. Rule for Addition and Subtraction Calculating with Numbers Written in Scientific Notation
In order to add or subtract numbers written in scientific
notation, you must express them with the same power of 10.
(Same characteristic). Then correct to proper scientific notation.
Sample Problem: Add 5.8 x 103 and x 104
(5.8 x 103) + (21.6 x 103) =
27.4 x 103
2.74 x 104
Exercise: Add 8.32 x and 1.2 x 10-5
1.28 x 10-5