1. Chapter 2, Measurements and Calculations
2.1 Scientific Notation
2.2 Units
2.3 Measurements of Length, Volume, and Mass
2.4 Uncertainty in Measurement
2.5 Significant Figures
2.6 Problem Solving and Dimensional Analysis
2.7 Temperature Conversions; An Approach to Problem Solving
2.8 Density
LEARN THE RULES

2. Chapter 2, Measurements and Calculations
LEARN THE RULES
2.1 Scientific Notation
THE GIVEN
After moving decimal points everything is multiplied by 10 to some exponent
Take the original number and move the decimal point either right or left so that only one number, (1 to 9) remains to the left of the decimal point and looks like this
#.####.....
After moving the decimal point count the number of spaces you moved it and make this the exponent (E) attached to the 10
X 10E
If you moved the decimal to the left as described in Rule 1 make the Exponent (E) positive (+), if you moved the decimal to the right, make it negative (-)

3. Chapter 2, Measurements and Calculations
LEARN THE RULES
2.1 Scientific Notation
4,237.
35,230.
357, 249.
X 10 ___ 4 5 2 1 -4 -3 /
/ / /
/ /
4,237.
4, spot
4, spots
spots
X 103

4. Chapter 2, Measurements and Calculations
LEARN THE RULES
2.1 Scientific Notation
4,237.
35,230.
357, 249.
X 10 ___
X 10 ___
4,237.
4, spot
4, spots
spots
X 10 ___
X 10 ___
X 103
X 10 ___
X 10 ___

5. English – Metric - International
Chapter 2, Measurements and Calculations
English – Metric - International
2.2 Units
Meter-Liter-Gram 1 .1
.01
.001 10
100
1000
deci
centi
milli
deca
hecto
kilo
1 x 103
1 x 102
1 x 101
1 x 100
1 x 10-1
1 x 10-2
1 x 10-3
Down
Right Up
Left
English – United States
Metric – Most of the remaining Industrialized World
International – 1960 Agreement
Up Move Decimal Left
Down Move Decimal Right
INTERNATIONAL
Physical Quantity
Name of Unit
Abbreviation
Mass
Kilogram kg
Length
Meter m
Time
Second s
Temperature
Kelvin K

6. Chapter 2, Measurements and Calculations Understanding Metrics
2.3 Measurements of Length, Volume, and Mass
Understanding Metrics
Meter-Liter-Gram 1 .1
.01
.001 10
100
1000
deci
centi
milli
deca
hecto
kilo
1 x 103
1 x 102
1 x 101
1 x 100
1 x 10-1
1 x 10-2
1 x 10-3
Down
Right Up
Left
Up Move Decimal Left
Down Move Decimal Right
Area: (Length) (Width) or LxW EXPRESSED as 1) sq units 2) units squared, or 3) units2
Volume: (Length) (Width) (Height) or LxWxH EXPRESSED as 1) c units, 2) units cubed or 3) units3

7. Chapter 2, Measurements and Calculations Limited by the Equipment
2.4 Uncertainty in Measurement
Most measurements require a level of estimation because of the limits of the device (i.e., Ruler or Graduate Cylinder)
Most easily done by estimating the middle distance between two lines of demarcation as a half 1 2 3 4 5 6
Metric Ruler broken into cm
1 cm
1.9 cm
Estimating at the mid point of 2.4 cm and 2.5 cm we select 2.45 cm
It could in fact be 2.44 cm or 2.46 cm
This could be different if another person estimated it
There may be multiple measures of several did so
What if there were 5
2.45
2.46
2.44
The first two digits in each measurement are the same, These are CERTAIN numbers.
The third digit, estimated, is UNCERTAIN.
All CERTAIN numbers and the first UNCERTAIN number are what we record.
These are the SIGNIFICANT FIGURES
This ruler, with our estimation is deemed good to the 100ths place and assumed to be + 1 (the estimated number)

8. Chapter 2, Measurements and Calculations
How to Determine
2.5 Significant Figures
Rules for Rounding
If the digit to be removed
<5 the number remains the same (e.g., 1.33 rounds to 1.3)
=/> 5 the number increase by 1 (e.g., 1.35 rounds to 1.4)
In a series of calculations
Carry the extra digits to the end
Round the final answer
Rules for Significant Figures
Non-zero integers
Zeros
Leading zeros (those appearing before non-zero integers) never count
Captive zeros (those appearing between non-zero integers) always count
Trailing zeros (those at the right end of non-zero integers) count only when there is a decimal point
100 has 1 sig fig
100. has 3 sig figs
Exact Numbers
Counted, but not measured
Definitions (1 inch = 2.54 cm)
Rules for Significant Figures in Calculations
Multiplication and Division - Limited to the smallest number of sig figs in the numbers used in the operation (e.g., 4.56 x 1.4 = rounded to 2 sig figs because of 1.4, so the answer is 6.4)
Addition and Subtraction – The smallest number of decimal places (e.g., = rounded to 3 sig figs because 18.0 has only 1 decimal place, so the answer is 31.1)

9. Chapter 2, Measurements and Calculations
Give the number of significant figures for the following:
A sample of OJ contains g of Vitamin C. ____________
A hair weighed in a crime lab has a mass of g. ____________
The distance between two points is x 103 ft. ____________
100 runners began the race, but only 60 completed the course. ____________
Without performing the calculation, predict the number of sig figs there in the final answer.
Sum of
5.19
1.9
0.842
Difference of
1081 – 7.25
Product of
2.3 x 3.14
Cost of
3 Boxes of candy at $2.50 per box 2
Calculations using significant figures :
5.18 x = – 0.33 =
(3.60 x 10-3) x (8.123) ÷ 4.3 = x =

10. Chapter 2, Measurements and Calculations
Give the number of significant figures for the following:
A sample of OJ contains g of Vitamin C. ____________
A hair weighed in a crime lab has a mass of g. ____________
The distance between two points is x 103 ft. ____________
100 runners began the race, but only 60 completed the course. ____________
Without performing the calculation, predict the number of sig figs there in the final answer.
Sum of
5.19
1.9
0.842
Difference of
1081 – 7.25
Product of
2.3 x 3.14
Cost of
3 Boxes of candy at $2.50 per box
None after Dec 2 3 2
Calculations using significant figures :
5.18 x = – 0.33 =
(3.60 x 10-3) x (8.123) ÷ 4.3 = x =
3 aft Dec
1 aft Dec 2
1 aft Dec