Example 2 (don’t copy, just try) The automobile gas tank of a Canadian tourist holds L of gas. If 1 L of gas is equal to 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 = L Unknown = Conversion factors:

Example 2 Initial = L Unknown = $ (cost) Conversion factors:

Example 2 Initial = L Unknown = $ (cost) Conversion factors: L  gal: gal  $:

Example 2

Unknown = initial x c.f. x c.f.

Example 2 $ ? = L x c.f. x c.f. First c.f. must cancel out litres Must have L in the denominator (below)

Example 2

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 Lengthmetrem Massgramg VolumelitreL Timeseconds TemperaturekelvinK Amount of Substance molemol Written Prefix Prefix Symbol Equivalent Exponential megaM10 6 kilok10 3 hectoh10 2 dekada decid10 -1 centic10 -2 millim10 -3 microμ10 -6

SI Prefixes 5 Mm = 5x10 6 m 5 m = 5x10 -6 Mm 1.2 ms = 1.2x10 -3 s 12 s = 1.2x10 4 ms Written Prefix Prefix Symbol Equivalent Exponential megaM10 6 kilok10 3 hectoh10 2 dekada decid10 -1 centic10 -2 millim10 -3 microμ10 -6

Other Units & Equivalences 1 t = 1 tonne = 10 3 kg 1 mL = 1 cm 3 (cubic centimetres, cc) 10 3 L = 1 m 3

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 (m 2 ) Volume = length x width x height (m 3 )

Changing Units of Area & Volume Example: 10 m 3 = ? cm 3 Start with the metric conversion factor 1 m = 100 cm To get m 3 we have to square both sides (1 m) 3 = (100 cm) 3 Remember that the exponent applies to both the number and the units 1 3 m 3 = cm 3 1 m 3 = 10 6 cm 3

Changing Units of Area & Volume 10 m 3 = ? cm 3 We have just derived a conversion factor relating m 3 and cm 3 (1m 3 = 10 6 cm 3 ) 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 = g = 0.01 g Milligram = g = 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 b y3579 x0123 m = y 2 – y 1 x 2 – x 1