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