- Sit with, or near, your group & take out your
sig figs worksheet
- Talk to group members to see where you
want to sit
- Remember your number!
#
Group A
Group B
Group C
Group D
Group E
Group F
Group G
1
ANNA G.
NICOLA
BERNICE
JASMINE
KOMAL
MANISHA
BEN
2
IVAN
VIVI
ANNA Z.
IVY
NICOLE
TIAN
WING
3
TOMMY
ECKHAM
SIMRAN
ANGELA
KIANA
DOM
NANCY
4
DEBORAH
HUSN
RAFAY
AUTUMN
VERONICA
JONATHAN
FELIPE & AMY
• Hand in Course Outline, Safety Agreement, Contact
Lens Letter on the overhead please
• New students: measurement lab at lunch today,
safety quiz tomorrow at lunch
• Was it helpful to post up the notes a day
beforehand?
• I will try to do this every class so you can print, take
notes or read it over before class
Today’s Groups
• When I ask you to go into groups to try questions
today, discuss the solution in your group
• Make sure everyone understands the steps
• I pick a number, that number from every group
stands up, I pick one (or more) to write answers on
the board
• No notes allowed when you come up to write
• Get into your groups and remember your numbers
Mixed Operations with Sig Figs
• Follow the rules for each operation
• Do NOT round off after every step
• Do keep track of the decimal places and sig figs
every calculation you make
• Try:
9.34 x 0.07146 – 6.88 x 0.08115
Mixed Operations with Sig Figs
9.34 x 0.07146 – 6.88 x 0.08115
= 0.6674364 – 0.558312
Mixed Operations with Sig Figs
9.34 x 0.07146 – 6.88 x 0.08115
= 0.6674364 – 0.558312
= 0.1091244
Mixed Operations with Sig Figs
9.34 x 0.07146 – 6.88 x 0.08115
= 0.6674364 – 0.558312
= 0.1091244
= 0.109
Try Hebden p.40 #59 c, f, g
Work with your groups!
Dimensional Analysis
(Unit Conversions)
Conversion Factors
• A conversion factor is a fraction relating 2 units
without changing the actual quantity
• E.g. 1 min = 60 s can be written as the conversion factor
1 min
60 s
of
or
60 s
1 min
• Note the quantity (amount of time) in 1 min and 60s are
the same, they are just expressed using different units
Same Quantity, Different Units
Sig Figs in Conversion Factors
• How many sig figs in the numbers of
1 min
60 s
?
Sig Figs in Conversion Factors
• How many sig figs in the numbers of
• (1 sig fig)/(1 sig fig) you say?
1 min
60 s
?
Sig Figs in Conversion Factors
• How many sig figs in the numbers of
1 min
60 s
• (1 sig fig)/(1 sig fig) you say? Nope!
• Recall: sig figs are all the certain digits of a
measurement plus the 1st uncertain digit
?
Sig Figs in Conversion Factors
• How many sig figs in the numbers of
1 min
60 s
?
• (1 sig fig)/(1 sig fig) you say? Nope!
• Recall: sig figs are all the certain digits of a
measurement plus the 1st uncertain digit
• How certain are we that there are 60 s in 1 min?
Exact/Defined/Counting Numbers
• Exact/defined/counting numbers have infinite sig
figs and are not considered when doing calculations
•
1 min
60 s
is an exact conversion factor because there
are exactly 60 s in 1 min (not 60.000001 or
59.999999999 but 60.00000000000000000000…)
• There is no rounding and there is no uncertainty
• Other examples: 12/dozen, 2/pair, 1 m = 100 cm,
1 ft = 12 in
Exact/Defined/Counting Numbers
• Warning: not all conversion factors are exact
• Can you think of an example of an inexact
conversion factor?
Exact/Defined/Counting Numbers
• Warning: not all conversion factors are exact
• Can you think of an example of an inexact
conversion factor?
• Conversions between metric & imperial units
• E.g. 1 m = 3.2808 ft
• This number is rounded to 5 sig figs but goes on forever
• There is uncertainty so the number of sig figs matter
Exact/Counting or
Measured (Inexact)?
• 29 students in the classroom
• $20.48 in my pocket
• 100,000 hairs on my head
Exact/Counting or
Measured (Inexact)?
• 29 students in the classroom - exact
• $20.48 in my pocket
• 100,000 hairs on my head
Exact/Counting or
Measured (Inexact)?
• 29 students in the classroom - exact
• $20.48 in my pocket - exact
• 100,000 hairs on my head
Exact/Counting or
Measured (Inexact)?
• 29 students in the classroom - exact
• $20.48 in my pocket - exact
• 100,000 hairs on my head - exact
Solving Unit Conversion Problems
• Step 1: identify the initial amount – what info are you
given?
• Step 2: identify the unknown amount – what are you
looking for?
• Step 3: identify the conversion factor – how are 1 & 2
related?
• Overall: unknown amount = initial amount x conversion
factor
Example 1
• How many min are there in 3480 s?
• Step 1:
• Step 2:
• Step 3:
Example 1
• How many min are there in 3480 s?
• Step 1: initial = 3480 s
• Step 2:
• Step 3:
Example 1
• How many min are there in 3480 s?
• Step 1: initial = 3480 s
• Step 2: unknown = min
• Step 3:
Example 1
• How many min are there in 3480 s?
• Step 1: initial = 3480 s
• Step 2: unknown = min
• Step 3: conversion factor between min & s =
or
60 s
1 min
(which one do we use?)
1 min
60 s
Example 1
• How many min are there in 3480 s?
• Step 1: initial = 3480 s
• Step 2: unknown = min
• Step 3: conversion factor between min & s =
1 min
60 s
• Use the one with the unit you want on top (numerator)
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• ? min = 3480 s x conversion factor
• Want to leave min and cancel s so use the c.f. with
min on top (numerator) and s below (denominator)
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• ? min = 3480 s x
1 min
60 s
• Want to leave min and cancel s so use the c.f. with
min on top (numerator) and s below (denominator)
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• ? min = 3480 s x
1 min
60 s
• Want to leave min and cancel s so use the c.f. with
min on top (numerator) and s below (denominator)
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• ? min = 3480 s x
1 min
60 s
• Want to leave min and cancel s so use the c.f. with
min on top (numerator) and s below (denominator)
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
• Done?
1 min
60 s
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
1 min
60 s
• Done? NO! Sig figs!
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
1 min
60 s
• ? sig figs = ? sig figs x ? sig figs
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
1 min
60 s
• ? sig figs = 3 sig figs x ? sig figs
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
1 min
60 s
• ? sig figs = 3 sig figs x ∞ sig figs
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58 min = 3480 s x
1 min
60 s
• 3 sig figs = 3 sig figs x ∞ sig figs
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58.0 min = 3480 s x
1 min
60 s
• 3 sig figs = 3 sig figs x ∞ sig figs
Example 1
• How many min are there in 3480 s?
• Overall: unknown = initial x conversion factor
• 58.0 min = 3480 s x
• Now are we done?
1 min
60 s
Example 2 (don’t copy, just try)
The automobile gas tank of a Canadian tourist holds
39.50 L of gas. If 1 L of gas is equal to 0.264 gal in the
US (“gal” is the symbol for “gallon”), and gas is
$1.26/gal in Dallas, Texas, how much will it cost the
tourist to fill his gas tank in Dallas?
Example 2
Initial =
Unknown =
Conversion factors:
Example 2
Initial = 39.50 L
Unknown =
Conversion factors:
Example 2
Initial = 39.50 L
Unknown = $ (cost)
Conversion factors:
Example 2
Initial = 39.50 L
Unknown = $ (cost)
Conversion factors:
L  gal:
gal  $:
Example 2
Initial = 39.50 L
Unknown = $ (cost)
Conversion factors:
L  gal:
gal  $:
1L
0.264 gal
or
0.264 gal
1L
Example 2
Initial = 39.50 L
Unknown = $ (cost)
Conversion factors:
L  gal:
1L
0.264 gal
gal  $:
1 gal
$1.26
or
or
0.264 gal
1L
$1.26
1 gal
Example 2
• Unknown = initial x c.f. x c.f.
Example 2
• $ ? = 39.50 L x c.f. x c.f.
• First c.f. must cancel out litres
• Must have L in the denominator (below)
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x c.f.
• First c.f. must cancel out litres
• Must have L in the denominator (below)
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x c.f.
• First c.f. must cancel out litres
• Must have L in the denominator (below)
Example 2
• $ ? = 39.50 x
0.264 gal
1
x c.f.
• Second c.f. must cancel out gallons
• Must have gal in the denominator (below)
Example 2
• $ ? = 39.50 x
0.264 gal
1
x
$1.26
1 gal
• Second c.f. must cancel out gallons
• Must have gal in the denominator (below)
Example 2
• $ ? = 39.50 x
0.264 gal
1
x
$1.26
1 gal
• Second c.f. must cancel out gallons
• Must have gal in the denominator (below)
Example 2
• $ ? = 39.50 x
0.264
1
x
$1.26
1
• Do we have the units we want for our unknown?
• Yes  we don’t need anymore conversion factors
• No  we need more conversion factors
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
• Finally: use calculator and express in correct sig figs
• ? s.f. = ? s.f. x ? s.f. x ? s.f.
• Are these conversion factors exact?
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
• Finally: use calculator and express in correct sig figs
• ? s.f. = ? s.f. x ? s.f. x ? s.f.
• Are the c.f.’s exact? 1st one no, 2nd one yes
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
• Finally: use calculator and express in correct sig figs
• ? s.f. = 4 s.f. x 3 s.f. x ∞ s.f.
• Are the c.f.’s exact? 1st one no, 2nd one yes
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
• Finally: use calculator and express in correct sig figs
• 3 s.f. = 4 s.f. x 3 s.f. x ∞ s.f.
• Are the c.f.’s exact? 1st one no, 2nd one yes
Example 2
• $ ? = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
• Finally: use calculator and express in correct sig figs
• 3 s.f. = 4 s.f. x 3 s.f. x ∞ s.f.
• $13.1 = 39.50 L x
0.264 gal
1L
x
$1.26
1 gal
Tips to Avoid Rounding Errors
• Write only one equation for the entire question
• If you must do more than one equation, do not
round before you get to the final answer
• Instead, write down as many digits as you can or
use the memory function on your calculator (M+)
• This is the difference b/t right and wrong answers!
SI Units
• The International System of Units (Le Système
International d’Unités)
• Modernized version of the metric system used in
science
• Any SI prefix can be used with any SI base unit
SI Units
SI Prefixes
Quantity
Unit
name
Unit
Symbol
Length
metre
m
Mass
kilogram
kg
Volume
litre
L
Time
second
s
Temperature
kelvin
K
Amount of
Substance
mole
mol
Electric
current
ampere
A
Written
Prefix
mega
Prefix
Symbol
M
Equivalent
Exponential
106
kilo
hecto
k
h
103
102
deka
deci
centi
da
d
c
101
100
10-1
10-2
milli
micro
m
μ
10-3
10-6
SI Prefixes
Written
Prefix
mega
Prefix
Symbol
M
Equivalent
Exponential
106
kilo
hecto
k
h
103
102
deka
deci
centi
da
d
c
101
100
10-1
10-2
milli
micro
m
μ
10-3
10-6
• 5 Mm = 5x106 m
• 5 m = 5x10-6 Mm
• 12 ms = 1.2x10-3 s
• 12 s = 1.2x103 ms
Other Units & Equivalences
• 1 t = 1 tonne = 103 kg
• 1 mL = 1 cm3 (cubic centimetres, cc)
• 103 L = 1 m3
Derived Units
• A unit made by combining two or more other units
• Speed = distance/time = km/h
• Density = mass/volume = g/L
Group Activity
• Closed book, open notes
• I give questions
• 5 min to discuss the solution in your group
• Make sure everyone understands the steps
• I pick a number, that number from every group
stands up, I pick one (or more) to write answers on
the board
• No notes allowed when you come up to write
• Get into your groups and remember your numbers
Question 1
• Express 905 in 2 sig figs
Question 1
Express 905 in 2 sig figs
= 9.0 x 102
Question 2
1.805 x 104 + 5.89 x 102 = ?
Question 2
1.805 x 104 + 5.89 x 102 = ?
Always convert smaller exponent to the bigger one
1.805 x 104 + 0.0589 x 104 = 1.864 x 104
Question 3
25.00 x 0.1000 – 15.87 x 0.1036
Question 3
25.00 x 0.1000 – 16 x 0.1036
= 2.500 – 1.6576
= 0.8424
= 0.8
Question 4
• If there are 6.02 x 1023 atoms in 1 mol of atoms,
how many atoms are there in 5.5 mol of atoms?
Question 4
• If there are 6.02 x 1023 atoms in 1 mol of atoms,
how many atoms are there in 5.5 mol of atoms?
Question 5
• Sugar costs $0.980/kg. 1 t = 1000 kg. How many
tonnes (“t”) of sugar can you buy for $350?
Guiding Questions for the Video
• What are the differences between exact and
measured numbers?
• What are the two kinds of 0’s and how do we tell
them apart?
• Are there disagreements between the video and
your notes?
• Hand in tomorrow: sig figs worksheet, Hebden p.
14 #2-10
• Practice: Hebden p.19-22 #11-18
• Start studying for unit 1 test on Monday
• Tomorrow will be a fun review activity