1. TWO METHODS OF OBSERVATION
Qualitative observations describe Quantitative observations measure
• Slightly rough surface • Mass = 23.6 grams
• Round • Volume = 38.4 ml
• Grayish brown • Density = 0.615 g/ml

2. QUANTITATIVE MEASUREMENT
Quantitative data requires a standard unit of measure
• SI unit: uses meters, kilograms, seconds
• Principal system used in scientific work; What we will be using in class
• English units: uses feet, pounds, seconds
Length Mass Time
SI Unit
(System Meters (m) Kilograms (kg) Seconds (s)
International)
Measuring devices Electric balance, spring
Ruler
scale, triple beam stopwatch
Measuring stick
balance
Original Standard 1/10,000,000 of distance Mass of 0.001 cubic meters
0.001574 average solar days
from equator to North Pole of water
Current Standard 9,192,631,770 times the period of a
Distance traveled by light in Mass of a specific platinum-
radio wave emitted from a cesium-
a vacuum in 3.34 x 10-9 s iridium alloy cylinder
133 atom

3. SI UNIT PREFIXES
• In the SI units, the larger and smaller units are defined in multiples of
10 from the standard unit.
• See table 1-4 (pg. 11) for complete table
prefix mega kilo hecto Deka Deci Centi Milli micro
Meter
Gram
Value 106 103 102 101 Second 10-1 10-2 10-3 10-6
Liter
m
Abbrev- g
M k h da d c m μ (“mew”)
iation s
l

4. PRECISION & ACCURACY
• Based on the definitions of precision and accuracy, describe the following pictures as
being: 1) precise or imprecise, 2) accurate or inaccurate

5. UNDERSTANDING SCIENCE
• In physics, we typically understand our world through measurement and developing
quantitative relationships (equations) between physical quantities
• There is uncertainty in all measurements:
• Blunders, human error
• Limitation in accuracy of measuring device
• Inability to read device beyond smallest division
• Manufacturing of device
• Two factors to consider in quantitative measure: the accuracy & precision

6. MEASUREMENTS IN SCIENCE
• Precision: the degree of exactness with which a measurement is
made.
• Two ways to describe precision:
1. How close measured values are to one another
• Ex: Given 2 sets of data: Precise
Imprecise Precise
7.35ml
7.35ml 7.35ml
7.33ml
6.94ml 7.33ml
7.34ml
8.23ml 7.34ml
7.33ml
7.37ml 7.33ml
• Standard deviation (a measure of how spread out numbers are)
2. The number of decimal places used to express a value
• Ex: a measurement of 23.5 cm is less precise than 23.453 cm

7. PRECISION
• When measuring, the precision of a measure depends on the measuring device
used.
• Precision of a measuring device = smallest division on the device
• However, we can estimate to an extra decimal past this!
• Looking at the ruler below…what is the precision of the ruler in cm? What is the
measurement at the arrow?
Measurement is 4.34 cm
Precision of ruler is
0.1 cm

8. MEASURING IN SCIENCE
8.24 cm
Precision: 0.1 cm 52.8 ml
Precision: 1 ml
(measure from bottom of meniscus)

9. MEASURING IN SCIENCE
• Accuracy: How close a measured value is to the true value of the quantity
measured.
• Accuracy is affected by:
• Lack of calibration or error in measuring instrument
• Human error in measurement
• Ex: reaction time in measuring time, etc.
• Minimized by conducting multiple trials
• Relative error tells us the accuracy of a measure.

10. SIGNIFICANT FIGURES
• Defined as the number of reliably known digits in a number.
Rules for determining significant figures: figures:
• Rules for determining significant Examples
1. Zeros between other nonzero digits are significant 50.3 m
3.0025 s
2. Zeros in front of nonzero digits are not significant 0.893 kg
0.00008 ms
3. Zeros that are at the end of a number and to the right of the 57.00 g
decimal are significant 2.000000 kg
4. Zeros at the end of a number to the left of a decimal are 1000 m
significant if they have been measured, are the first estimated (could have 1 or 4 significant
digit, or are hatted; otherwise, they are not significant. figures. We will say it has 1
sig figs)
100Ō m

11. SIGNIFICANT FIGURES
An alternative way of determining significant figures: Atlantic / Pacific rule
• Is the decimal point present or absent?
Pacific: Decimal is Atlantic / Pacific Rule Atlantic: Decimal is
present absent
• Start counting sig figs • Start counting from
from left starting with right with first nonzero
first nonzero digit. Keep digit. Keep counting
counting until you run until you run out of 1-9
out of 1-9 digits digits
0.0006 => 1 sig fig 40,000 => 1 sig fig
0.00935 => 3 sig figs 1,040 => 3 sig figs
1.020 => 4 sig figs 1,200,100 => 5 sig figs

12. SIGNIFICANT FIGURES
• Hatted zeros indicate significant zero digits
Digit Explanation
2000 - Start from first nonzero, nonhatted digit from right => 1 sig fig
2Ō00 - Start from first nonzero nonhatted digit from right => 2 sig figs
2000. - Start from first nonzero digit from left
- 4 sig figs

13. SIGNIFICANT FIGURES
• Try these out: • Answers
• 1020 • 3
• 3300 • 2
• .0012 • 2
• 3000 • 4
• 5.0020 • 5
• 1.00 • 3
• 80,000 • 1
• 0.100 • 3

14. LAB ACTIVITY: HOW FAR DID YOU GO?
• Throughout time, are system of
measuring has evolved a number of
times.
• The inch evolved from the
barleycorn
• The mile evolved from the furlong
(the distance a plough team could
be driven without rest; 8 furlongs = 1
mile)
• Today, you will use 1 or 2 objects of your
choosing to measuring an unknown
distance
• You will then convert this to meters as a
way to study precision & accuracy.

15. Farm-derived units of measurement:
The rod is a historical unit of length equal to 5½ yards. It may have originated from the
typical length of a mediaeval ox-goad.
The furlong (meaning furrow length) was the distance a team of oxen could plough
without resting. This was standardised to be exactly 40 rods.
An acre was the amount of land tillable by one man behind one ox in one day.
Traditional acres were long and narrow due to the difficulty in turning the plough.
An oxgang was the amount of land tillable by one ox in a ploughing season. This could
vary from village to village, but was typically around 15 acres.
A virgate was the amount of land tillable by two oxen in a ploughing season.
A carucate was the amount of land tillable by a team of eight oxen in a ploughing
season. This was equal to 8 oxgangs or 4 virgates.
Source: "Furlong." Wikipedia. Wikimedia Foundation, 09 June 2012. Web. 06 Sept.
2012. <http://en.wikipedia.org/wiki/Furlong>.

16. SIGNIFICANT FIGURES WITH MATH OPERATIONS
• When adding or subtracting, the precision matters!
• your answer can only have as many decimal positions as the value with the least number of
decimal places
1.2003 ml + 23.25 ml = 24.45 ml
NOTE: calculators DO NOT give values in the correct number of significant digits!

17. SIGNIFICANT FIGURES WITH MATH OPERATIONS
• When multiplying or dividing, significant figures matter!
• your answer can only have as many significant figures as the value with the least number of
significant figures.
3.6 cm x 0.01345 cm = 0.048 cm 2
• Must determine the number of significant figures in the numbers being multiplied/divided
• NOTE: calculators DO NOT give values in the correct number of significant digits!

18. MATH OPERATIONS WITH SIGNIFICANT FIGURES
• Try these: • Try these:
16 x 2 20 4001 + 3.8 = 4005
1.35 x 400. 540.
24.38+0.0078 = 24.39
10,002 x 0.034 340
300÷5.0 60 10.9
15.3– 4.38=
350.÷17.7 19.8
100.– 3.2= 97
11.40– 3.8= 7.6

19. SCIENTIFIC NOTATION
• When expressing an extremely large number such as the mass of Earth, or a very small
number such as the mass of an electron, scientists use the scientific notation.
• For example, the mass of Earth is about 6,000,000,000,000,000,000,000,000 kg
and can be written as 6 X 1024 kg.
• Makes it clear which figures in a
number are significant.

20. MEASURING: SCIENTIFIC NOTATION
• Scientific notation converts a number from standard form to one digit, a decimal
point, and a power of 10
• To convert from standard form to scientific notation:
• Move decimal point so that number is one decimal form
• Power of 10 = number of spaces moved
• If moved to left , exponent is +
• If moved to right , exponent is -
• Examples:
1 = 1x100
10 = 1x101
100 = 1x102 1/10 = 0.1 = 1x10-1
1000 = 1x103 1/100 = 0.01 = 1x10-2

21. SCIENTIFIC NOTATION
• Example 1: Convert 3,020 to scientific notation.
• Solution:
• Significant figures must be conserved. How many significant
figures are there?
• Move the decimal so that there is one digit before the
decimal.
• The decimal must be moved by 3 positions to the right
• Will the exponent be positive or negative?
• The exponent will be positive3since 3,020 is greater than one.
3.02 x 10

22. SCIENTIFIC NOTATION
• Example 2: Convert .0003070 to scientific notation.
Solution:
• Significant figures must be conserved. How many significant
figures are there?
• Move the decimal so that there is one digit before the
decimal.
• Will the exponent be positive or negative?
• The exponent will be negative since the number is less than
one.
3.070x10 -4 Notice how the zero remains at the
end to show that it is significant!

23. SCIENTIFIC NOTATION
• Convert the following to scientific notation with correct sig figs.
1. 346,000
3.46 x 105
2. 0.0210
2.10 x 10-2
3. 0.00000900
9.00 x 10-6
4. 500,Ō00
5.000 x 105

24. SCIENTIFIC NOTATION
Converting from scientific notation to standard form:
1. Identify & preserve all sig figs from scientific notation
2. Move decimal the number of spaces of the exponent
• If exponent is POSITIVE +, move decimal to RIGHT 
• If exponent is NEGATIVE -, move decimal to LEFT 
• Examples:
Scientific Operations Standard
Notation notation
8.75 x 10-2 - 3 sig figs 0.0875
- Negative exponent - move decimal to left
3.635 x 105 - 4 sig figs 363,500
- Positive exponent – move decimal to right
2.50 x 102 - 3 sig figs 250. OR
- Positive exponent – move decimal to right 25Ō

25. Scientific Notation on a calculator
• Use the “EE” key to do
scientific notation on a
calculator

26. MEASURING: SCIENTIFIC NOTATION
• Identify the number of significant figures and convert the
number to standard notation for the following:
Sig Figs Standard Form
1.52 x 103 3 1520
7.30 x 10-3 3 0.00730
6.75 x 105 3 675000
5.3030 x 10-2 5 0.053030
3.670 x 105 4 367Ō00

27. SCIENTIFIC NOTATION
Mathematical operations with significant figures for
scientific notation
Same rules apply
Operation (rule) Operation Examples
Multiplication /
Division
Multiplication:
10a(10b) = 10a + b
(1.5´10 ) (1.2 ´10 ) = (1.5) (1.2) (10 ) (10 ) =1.8´10
3 4 3 4 7
(Input with lowest # of sig 2 sf 2sf 2 sf
figs limits output to that
Division: (3.5´10 ) = æ 3.5 ö 10 10 = 0.83´10
3
÷( ) (
number of sig figs ) a ç ) 3 -4 -1
= 8.3´10-2
10
= 10 a-b ( 4.20 ´10 ) è 4.20 ø
4
10 b 2 sf / 3 sf 2 sf
Note: exponent in denominator becomes negative
Addition / Subtraction Must change 7.4 x 10-3 7.4 x 10-3 (2 sig figs)
(Output is as precise as exponents to be the -3.5 x 10-4 -0.35 x 10-3 (2 sig figs)
least precise input) same before 7.05 x 10-3 7.1x10-3 (2 sf)
performing operation
2.35 x 105 2.35 x 105 (3 sig figs)
+ 3.70 x 103  + 0.0370x105 (3 sig figs)
2.3870x105  2.39x105 (3 sf)

28. MEASURING: SIGNIFICANT FIGURES
• Try these: • Try these:
4001
16 x 2 20 + 3.8 4005
1.35 x 400.
540. 24.38
10,002 x 0.034 24.39
+0.0078
340
300 15.3
= 60 10.9
– 4.38
5.0
350. 19.8
= 100.
17.7 – 3.2 97
11.40
– 3.8 7.6

29. MEASURING: SIGNIFICANT FIGURES
Mathematical operations with significant figures for
scientific notation
Same rules apply
Operation (rule) Operation Examples
Multiplication /
Division
Multiplication:
10a(10b) = 10a + b
(1.5´10 ) (1.2 ´10 ) = (1.5) (1.2) (10 ) (10 ) =1.8´10
3 4 3 4 7
(Input with lowest # of sig 2 sf 2sf 2 sf
figs limits output to that
Division: (3.5´10 ) = æ 3.5 ö 10 10 = 0.83´10
3
÷( ) (
number of sig figs ) a ç ) 3 -4 -1
= 8.3´10-2
10
= 10 a-b ( 4.20 ´10 ) è 4.20 ø
4
10 b 2 sf / 3 sf 2 sf
Note: exponent in denominator becomes negative
Addition / Subtraction Must change 7.4 x 10-3 7.4 x 10-3 (2 sig figs)
(Output is as precise as exponents to be the -3.5 x 10-4 -0.35 x 10-3 (2 sig figs)
least precise input) same before 7.05 x 10-3 7.1x10-3 (2 sf)
performing operation
2.35 x 105 2.35 x 105 (3 sig figs)
+ 3.70 x 103  + 0.0370x105 (3 sig figs)
2.3870x105  2.39x105 (3 sf)