1. Significant Figures and Scientific notation
Chapter 2 review
Significant Figures and Scientific notation

2. Scientific notation (SN)
Rules for SN
Nx10n
N-any number between 1-9.9
n- how many places decimal point moves
big # are positive
small #are negative

3. Examples Starting with the decimal move it over six places
Starting with the last zero move the decimal over eight places
= 8.2 x 10-6
Starting with the decimal move it over six places

4. Rules for counting significant Figures
1-9 always SF
0 in front NEVER SF
0 in middle ALWAYS SF
0 at end SF if decimal exists
0 at the end without decimal are “ambiguous” not SF
0.0035
2 SF are present b/c 0 in front do not count
6 SF are present 0 in middle are SF

5. Rule Number one examples
Numbers 1-9 are always significant figures
1,756 = 4 significant figures
3, = 8 significant figures
2,999,675,843 = 10 significant figures
Always

6. Rule number two examples
Zero’s in front are never significant figures
= 2 significant figures
= 3 significant figures
= 1 significant figure
Never

7. Rule number three examples
Zero’s in the middle are always significant figures
3045 = 4 significant figures
40098 = 5 significant figures
403 = 3 significant figures
Always

8. Rule number four examples
Zero’s at the end are always a significant figure if there is a decimal point
= 6 significant figures
4.00 = 3 significant figures
38.00 = 4 significant figures
Always

9. Rule number five examples
Zero at the end is ambiguous and is not a significant figure
23000 = 2 significant figures
200 = 1 significant figure
13400 = 3 significant figures
Never

10. Adding/subtracting Significant figures
Keep as many SF as the least precise number
Add/subtract all the numbers according to rules of SF Ex
15.7
37.514
12,000
Least precise
Least precise
13,284.56
1.3x104
37.5 or 3.75x101

11. Multiply/divide significant figures
Keep the lowest number of SF
Ex.
(125)(0.23)= (least number of SF) =
56.6
2 sf
3 SF
7.18x10 -3

12. Rounding
If the number you are rounding is followed by 5,6,7,8,9 then round the number up
If the number you are rounding is followed by 0,1,2,3,4 then leave it
Ex. 2,158,346 in scientific notation to three SF x 106 (round up because of the 8 after the 5)
Ex round to 3 SF (round to 100. because of the 0 after decimal)

13. Exact numbers
Exact numbers are those that have defined values or are integers that result from counting numbers of objects.
Exact numbers have infinite number of SF
Example:
one dozen eggs is exactly 12 eggs
1000 grams is exactly 1 kilogram
2.54 centimeters is exactly 1 inch

14. Inexact numbers
Inexact numbers are approximate numbers or numbers obtained from measurements.
Example:
One mile is kilometers
One ounce is grams
One kilogram is pounds