How do I
read the
equipment?
What is the Volume?
Reading Graduated Equipment
(ie. grad cylinders, thermometers…)
 See
skills sheet
•Read one value
better than the
markings
•Estimate between
markings
Measurement:
5.22 cm
________
•If on the mark,
include a zero after
last value recorded
Measurement:
1.70 mL
________
Significant Figures
(Sig Figs)
Quantity includes all known digits plus
one estimated digit = last digit of #
 Indicates precision
 500 vs 500.01

Rule 1: All digits recorded from a lab
measurement are called significant figures.
Now the ZEROS!!!!
Rule 2: All non-zero digits are considered
significant.
measurement



96 g
61.4 g
0.52 g
number of sig figs
2
_________
3
_________
2
_________
Rule 3: Middle zeros are always significant.
SANDWICH RULE
measurement



5.029 m
306 cm
410.0 g
number of sig figs
4
_________
3
_________
4
_________
Rule 4: A leading zero is never significant. The
zeros are place holders only.
measurement



number of sig figs
1
.0007 g
________
3
0.00783 kg ________
6
5.00783 kg ________
Rule 5: Trailing zeros are significant only when
to the right of decimal point.
measurement



number of sig figs
3
47200 km ________
5
4.7200 km ________
3
82.0 m
________
820. M
_________
Rule 6: All significant figures include units.
Rule 7: All numbers multiplied by 10 in
scientific notation are considered significant.
measurement


number of sig figs
4
3.600 x 103 m _________
3
1.02 x 10-9 g
_________
SAME RULES: SHORT CUT “The Arrow Rule”: Draw an arrow to
the first significant digit and count significant figures.
Atlantic
Ocean
Pacific
Ocean
decimal Present
measurement
decimal Absent
# sig figs
measurement
# sig figs
61.4 g
____
3
306 cm
____
3
0.52 g
2
____
7 000 g
1
____
82.0 m
3
____
5
50 002 pennies ____
3
0.00783 kg ____
Practice: how many sig figs in each quantity?
45.35 km
6.2100 dag
1.22 us
8 000 000 m/s
0.034567 ML
4
5
3
1
5
# of sig figs in answer is based on # sig figs in least precise
measurement
Which is the least precise, 7.22 m or 7.22555 m?
_______
7.22
m
Rules for multiplication and division:
1)
Count the # of sig figs in each measurement.
2)
Use least # sig figs for # of digits in answer.
Examples:
4.5 cm X 2.54 cm X 3.215 cm = 36.74745
37 cm3
answer w/ sig figs ______________
4.62 g
=
0.308 g/cm3
15.00 cm3
0.308 g/cm3
answer w/ sig figs __________
2
2.124 mm X 65mm = 138.06 mm
answer w/ sig figs _____________________________
140 mm2 or 1.4 x 102 mm2
Data Analysis
Accuracy & Precision
“Numerical precision is the very soul of science.”
Precision




How reproducible (repeatable)
how consistently that measurement is made
Smaller the range = more precise
To find Precision calculate percent error.
% error =
Avg experimental – accepted
Value
value
Accepted value
x 100
Which is most precise?
…least precise?
most
least
Most precise instrument for
liquid volume measurement
Volumetric
flask
Which is most precise?



Equipment had markings every 2 or more mL
19 ml
Equipment had markings every 1 mL
19.5 ml
19.50 ml Equipment had markings every 0.1 mL
Estimated
digit
More digits means more divisions
(markings on the equipment)
Find % error


Average = 3.8
Accepted = 2.2
% error =
[3.8 - 2.2]
x 100
2.2
= 73%
Accuracy


How close to the correct value (accepted value)
To find accuracy, compare average to accepted value
Sum of experimental values
Average =
# of values
Which set of values is more
accurate if 7.6 is correct?
Set One
 7.0
Avg = 8.3
 8.1
 9.8
Set Two
 6.3
 8.0
 7.9
Avg = 7.4
Which ones are precise?
#1
Precise
#2
Precise
#3
NOT Precise
Which ones are accurate?
#1
#2
#3
Accurate
NOT accurate
NOT accurate
& precise
But precise
Or precise!
Which one is the most precise?
a
b
c
Which one is the most accurate?
Need to know how long a real meter is!
Try this one!
Trial 1
Trial 2
Trial 3
Average
Range
% error
Actual
Density
Density
3.6 g/ml
4.1 g/ml
3.8 g/ml
3.8 g/ml
3.6 to 4.1
73%
2.2 g/ml
Data Analysis cont
NUMBERS
“Numerical precision is the very soul of science.”
SCIENTIFIC NOTATION

EASY, right?

Change to sci not:

Diam of the sun: 1,392,000 km
1.392 x 106 km

Density of sun’s atoms: 0.000000028 g/cm3
2.8 x 10-8 g/cm3

Change back:

1.7 x 10-7 kg

-2.6 x 105 m
0.00000017 kg
-260,000 m
Rules for Scientific Notation

Move the decimal so that only one nonzero digit is
to the left of decimal

No non-significant zeros at end or before nonzero
digits
Remember sig
figs

Multiply by 10n where n = # places moved
–
–
n is + when decimal moves left (into sci not)
n is - when decimal moves right (into sci not)

Quantity

SI Base Units

can be measured
– A number AND a unit!
UNITS ARE
IMPORTANT!!!!!!!!!!!
SI Units (Systeme
Internationale d’Unites)
are standard
–





Time = second = s
Length = meter = m
Mass = kilogram= kg
Temp = kelvin = K
“Which one of these is not like the
others?”
Conversions btw. Units
M
Secret Worlds: The
Universe Within
k h dk BASE d c m
(compared to base unit)
BASE X 109 = giga = G
BASE X 106 = mega = M
BASE X 103 = kilo = k
BASE X 10-2 = centi = c
BASE X 10-3 = milli = m
BASE X 10-6 = micro = 
BASE X 10-9 = nano = n
BASE X 10-12 = pico = p

n
p
Give an example of
something that would
best be measured using
each prefix + grams and
meters.
5 x 10-2
Ex: 5 cm = ______m_
Derived Units



1 cm3
What is mL = _______?
formed by a combination of units
1 dm3 = 1 L
Density = mass = g = g
volume cm3 L
1L
1 mL
Factor Label Conversion
AKA Dimensional Analysis

Conversion factor – 2 quantities that are
equal to each other and arranged as a fraction
When Converting using factor labels
 Start with what you are given
 Always write your units
 Denominator is unit trying to get rid of
 Numerator is unit trying to change to
 Cross units out as they divide & cancel out
Example


12 inches = 1 foot
Conversion factors =
12 in
1 ft
•How many inches are in 15
feet?
12 in
15 ft
Or
= 180 in
x
1 ft
1 ft
12 in
Example #2
Butterfly wings: 1 wing has a mass of 00.56g
Conversion factors:

If you pulled the wings off of 28 butterflies, what
will be the total mass of wings you have.
(more than 1 step?)