- Sit with, or near, your group & take out your sig figs worksheet - Talk to group members to see...

- 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 Figs9.34 x 0.07146 – 6.88 x 0.08115= 0.6674364 – 0.558312

Mixed Operations with Sig Figs9.34 x 0.07146 – 6.88 x 0.08115= 0.6674364 – 0.558312= 0.1091244

Mixed Operations with Sig Figs9.34 x 0.07146 – 6.88 x 0.08115= 0.6674364 – 0.558312= 0.1091244= 0.109

Try Hebden p.40 #59 c, f, gWork 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 of or

• 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 sig fig)/(1 sig fig) you say?


• (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


• (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• 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



• $20.48 in my pocket - 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


• Step 1: initial = 3480 s

• Step 2:

• Step 3:

Example 1



• Step 2: unknown = min

• Step 3:

Example 1




• Step 3: conversion factor between min & s = or (which one do we use?)

Example 1




• Step 3: conversion factor between min & s = • Use the one with the unit you want on top (numerator)

Example 1


• Overall: unknown = initial x conversion factor

Example 1



• ? 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



• ? min = 3480 s x

• Want to leave min and cancel s so use the c.f. with min on top (numerator) and s below (denominator)

Example 1



• 58 min = 3480 s x

• Done?

Example 1



• 58 min = 3480 s x

• Done? NO! Sig figs!

Example 1



• 58 min = 3480 s x

• ? sig figs = ? sig figs x ? sig figs

Example 1



• 58 min = 3480 s x

• ? sig figs = 3 sig figs x ? sig figs

Example 1



• 58 min = 3480 s x

• ? sig figs = 3 sig figs x ∞ sig figs

Example 1



• 58 min = 3480 s x

• 3 sig figs = 3 sig figs x ∞ sig figs

Example 1



• 58.0 min = 3480 s x

• 3 sig figs = 3 sig figs x ∞ sig figs

Example 1



• 58.0 min = 3480 s x

• Now are we done?

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


L gal:

gal $:

Example 2


L gal: or

gal $:

Example 2


L gal: or

gal $: or

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 x c.f.

• First c.f. must cancel out litres

• Must have L in the denominator (below)

Example 2

• $ ? = 39.50 x x c.f.

• Second c.f. must cancel out gallons

• Must have gal in the denominator (below)

Example 2

• $ ? = 39.50 x x

• Second c.f. must cancel out gallons

• Must have gal in the denominator (below)

Example 2

• $ ? = 39.50 x x

• 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 x

• 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 x


• ? 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 x


• ? s.f. = 4 s.f. x 3 s.f. x ∞ s.f.


Example 2

• $ ? = 39.50 L x x


• 3 s.f. = 4 s.f. x 3 s.f. x ∞ s.f.


Example 2

• $ ? = 39.50 L x x


• 3 s.f. = 4 s.f. x 3 s.f. x ∞ s.f.

• $13.1 = 39.50 L x x

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 ofSubstance mole mol

Electric current ampere A

Written Prefix

Prefix Symbol

Equivalent Exponential

mega M 106

kilo k 103

hecto h 102

deka da 101

- - 100

deci d 10-1

centi c 10-2

milli m 10-3

micro μ 10-6

SI Prefixes

• 5 Mm = 5x106 m• 5 m = 5x10-6 Mm

• 12 ms = 1.2x10-3 s• 12 s = 1.2x103 ms

Written Prefix

Prefix Symbol

Equivalent Exponential

mega M 106

kilo k 103

hecto h 102

deka da 101

- - 100

deci d 10-1

centi c 10-2

milli m 10-3

micro μ 10-6

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 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

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