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: or

gal $:

Example 2

Initial = 39.50 L Unknown = $ (cost)Conversion factors:

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 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

• 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

• 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 x

• 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 x

• 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 x

• 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 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

Some SI Units SI Prefixes

Quantity Unit name

Unit Symbol

Length metre m

Mass gram g

Volume litre L

Time second s

Temperature kelvin K

Amount ofSubstance mole mol

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

• 1.2 ms = 1.2x10-3 s• 12 s = 1.2x104 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) • Area = length x width (m2)• Volume = length x width x height (m3)

Changing Units of Area & Volume

Example: 10 m3 = ? cm3 Start with the metric conversion factor

1 m = 100 cm To get m3 we have to square both sides

(1 m)3 = (100 cm)3 Remember that the exponent applies to both the number and the units

13 m3 = 1003 cm3 1 m3 = 106 cm3

Changing Units of Area & Volume

10 m3 = ? cm3

We have just derived a conversion factor relating m3 and cm3 (1m3 = 106 cm3)

Use this conversion factor to find the unknown just like before

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?

That’s the End of Unit 1…

• Unit 1 test Monday• Everything in Hebden Units I & II is fair game

except p.34 & 35 on Experimental Uncertainty• Everything in the PowerPoints are as well• Practice: all Hebden questions except #51 and

52

Unit Test Outline

• Lab safety, sig figs, scientific notation, measurements (how to record measurements, accuracy, precision, uncertainty), unit conversions

• Out of ~45-50 • Show as much work as you can, check sig figs

& units! • Scientific calculators ONLY

Lab Reports

• Very well done!

• Several groups went above and beyond

• Everyone got 10/10 and some feedback

• See me after class if you want to discuss

Station 1 – Volume (long, round things)

• What were the smallest divisions you could read on the instruments? These are your certain digits.

• Did you add an uncertain digit?• Burette scale is upside down (did you notice?)• Transferring from beaker to cylinder

– Less precise to more precise so there should’ve been more sig figs

Station 2 – Length (rulers and calipers)

• Calipers were the most precise because they gave the most decimal places

• You were asked to measure the diameter of a cork. Which diameter? How do you know if you’re really measuring the diameter?

Station 3 – Temperature

• Thermometers had Celsius AND Fahrenheit scales. Did your values match with the correct units?

• The other unit (the SI unit) for temperature is kelvin

Station 4 – Weight/Mass

• Centigram = 10-2 g = 0.01 g• Milligram = 10-3 g = 0.001 g• Always remember to zero your balance first

before weighing anything

Station 5 – Time

• Which was the most accurate? Trick question!

• You don’t know accuracy unless you have the true value!

• Just because two measurements were more precise doesn’t mean the other one which was way different can’t be more accurate

Linear Equations

• y = mx + b• m = slope

– Positive +– Negative –– Horizontal / Zero 0

• b = y-intercept y

x

by 3 5 7 9

x 0 1 2 3

m = y2 – y1

x2 – x1