1. Accuracy and Precision
Accuracy – how close a measured value is to the actual (true) value
Precision – how close the measured values are to each other
Low Accuracy
Low Precision
Low Accuracy
High Precision
High Accuracy
High Precision

2. Types of Error
Random Error – when you estimate a value to obtain the last sig fig for any measurement
Ex. Measuring the temperature to 1 decimal place using a thermometer
Systematic Error – happens due to an inherent error in the measuring system.
Ex. using a worn metre stick to measure your height

3. Significant Figures
Significant figures : the “important” digits in a numerical value.
the number contains all the digits that are certain plus one digit that is uncertain.
 Example: When a measurement is reported to be 47.5, that means the 4 and 7 are the certain numbers and the 5 is the uncertain numbers. It means that the actual value could be any number between 47.4 – 47.6.

4. Significant Figure Rules
Example
Significant Figures
1. Nonzero digits are always significant
1.254
4 sig. fig.
2. Leading zeros (zeros before any nonzero digits) are NOT significant
3 sig. fig.
3. Embedded zeros are significant
305.04
5 sig. fig.
4. Zeros’ behind the decimal point are significant
124.00
5 sig fig

5. State the number of significant figures in each of the followings:
Measurement
S.F.
967 e b
f. 9.3 c g
d. 5
h. 8.21

6. Rules for Sig Figs In Mathematical Operations
Multiplying and Dividing Numbers
In a calculation involving multiplication or division, the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied or divided.
e.g. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9 = 8 x 101

7. Rules for Sig Figs In Mathematical Operations
Adding and Subtracting Numbers
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
e.g = 4.0

8. Rules for Sig Figs In Mathematical Operations
Rounding Rules
1. If the digit after the one you want to keep is greater than 5, then round up.
e.g. To obtain 2 sig digs: 3.47 rounds to 3.5; rounds to 3.5
2. If the digit after the one you want to keep is less than five, then do nothing.
e.g. To obtain 2 sig digs: 3.44 rounds to 3.4; rounds to 3.4
3. If the single digit after the one you want is exactly 5, round to the closest even number.
e.g. To obtain 2 sig digs: 2.55 is rounded to 2.6; 2.25 is rounded to 2.2 e.g. BUT, is rounded to 2.3

9. Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
23 m2
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
2.4 x 102 m/s
lb x 3.23 ft
lb·ft
5.87 x 103 lb·ft
1.030 g ÷ 2.87 mL
g/mL
2.96 g/mL

10. Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m m
10.24 m
10.2 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL

11. Scientific Notation
A method used to express really big or really small numbers. Consist of two parts:
2.34 x 103
The first part of the number indicates the number of significant figures in the value.
The second part of the number DOES NOT count for significant figures.
This number is ALWAYS between and 10
The 2nd part is always 10 raised to an integer exponent

12. How its Done
1. Place the decimal point between the first and second whole number, and write ‘x 10’ after the number.
e.g. For 12345, it becomes 1.2 x 10
e.g. For , it also becomes 1.2 x 10
2. Indicate how many places you moved the decimal by writing an exponent on the number 10.
a) A move to the left means a positive move.
e.g. For 12345, it becomes 1.2 x 104
b) A move to the right means a negative move.
e.g. For , it becomes 1.2 x 10-4

13. The Fundamental SI Units
In all sciences, calculations are done using SI units (Le Système International d'Unités).

14. The Fundamental SI Units
Physical Quantity
Name
Abbr.
Length
meters m
Time
second s
Mass
kilogram kg
Temperature
Kelvin K
Amount of Substance
mole
Mol
Electrical Charge
Coulomb C

15. SI Prefixes
The international system of units consists of a set of units together with a set of prefixes.
Prefix
Mega
Kilo
Hecto
Deca
base
(g, m, L)
Deci
Centi
Milli
Micro
Symbol M k h da d c m 
Factor
106
103
102
101
100 = 1
10-1
10-2
10-3
10-6

16. Practice! Original Convert to… a) 3.15 m cm e) 955g kg b) 20.0Mg mg
f) 178mm
c) 75.4L ml
g) 650cm mm
d)1350mL L
h) 88.74ms s

17. Practice! Original Convert to… a) 3.15 m 315 cm e) 955g 0.955 kg
b) 20.0Mg
2.00 x 1010 mg
f) 178mm
17.8 cm
c) 75.4L mL
g) 650cm
6500 mm
Or 6.50X103 mm
d)1350mL
1.350 L
h) 88.74ms s

18. Dimensional Analysis SAMPLE PROBLEMS… Convert 7 years to seconds.
REMEMBER: Set up conversion factors to get rid of unneeded units, and to obtain needed units!
Conversion can be flipped if needed:
60 s
1min
1min
60 s 1 = =