Math tools: __________________ figures (digits) - tell you how ___________ a measurement is - _________ figures  ________ precise Significant precise more more

Ex 1: Measure the length of a box: 2 3 4 5 6 L = 4.7 cm = 4.7 ± 0.1 cm last digit is _____________ estimated

Ex 2: Use a “better” ruler: 1 2 3 4 5 6 L = 0.01 cm 4.67 cm = 4.67 ± last digit is ______________ estimated

Ex 3: Measure the length of a different box: 1 2 4 5 6 7 L = 6.49 cm = 6.49 ± 0.01 cm The precision is worthless because answer is _____________—not close to true or actual value. inaccurate

Figures (numbers) are significant if they are: any zeros that are: a/ between any _________________ numbers: 509; or b/ to the ___________ of a non-zero number AND to the ___________ of the decimal point: 0.00790; or c/ between a non-zero number and the __________ _________ : 10. non-zero significant right right decimal point Ex: number # sig. figs. # sig. fig. 5.3 6.6070 202900 3.00 x 108 0.008 40 0.67 40. 2 5 4 3 1 1 2 2

B. Sig. figs. when multiplying or dividing: answer has the _________ number of sig. figs., in this case: ____ ____ sig. figs. 3 lower 3.73 x 5.7 = 21 2 ____ sig. figs. 2 C. Sig. figs. when adding or subtracting: 3 18.541 +106.6 125.1 ___ decimal places 1 lower answer has the _________ number of ___________________ , in this case: ____ decimal places 1

II. Standard Scientific Notation: A. Moving the decimal point to left exponent is ___________ b/c number is _____ 1 5 616000 = 6.16 x 10 positive Shift ______ to here by ___ places left > ________ decimal pt. implied 5 B. Moving the decimal point to right exponent is ___________ b/c number is _____ 1 -3 0.0070 = 7.0 x 10 negative Shift ______ to here by ___ places right < 3

Ex: Convert to standard scientific notation number scientific notation 43000 0.0290 2012 0.5 80 80. 4.3 x 104 2.90 x 10-2 2.012 x 103 5 x 10-1 8 x 101 8.0 x 101

Units: In Regents Physics, we almost always use the _____ (International System) metric system. The ___________________ ,or most basic, units in this system are: SI fundamental quantity unit abbrev- iation length meter current ampere time second mass kilogram m A s kg "mAsk" The abbreviations spell _______________ (almost)

Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed. 1 bottom Ex: d = 15 nm rewrite as: d = 15 x _____ m prefix _________ represents ____ __________ for length (meters) with prefix without 5.3 km 1.7 cm 2.00 ms 1.21 GW 8.6 kg A trick b/c kg is already an SI unit

Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed. 1 bottom Ex: d = 15 nm rewrite as: d = 15 x _____ m 10-9 SI unit prefix _________ represents ____ symbol __________ for length (meters) 10-9 with prefix without 5.3 km 1.7 cm 2.00 ms 1.21 GW 8.6 kg 5.3 x 103 m 1.7 x 10-2 m 2.00 x 10-6 s A trick b/c kg is already an SI unit 1.21 x 109 W 8.6 kg

V. Converting Units: the power of "one" Ex: Convert 60 miles to kilometers. Use the conversion factor: 1 mi =__________ km This can be written as either: or Multiplying by either of these two factors does not change the ________________ (only the units) because both factors equal _______ . 1.609 1 mi 1.609 km 1.609 km 1 mi actual value one 1.609 km 1 mi Write: 60 mi x _________ = km 96.54 ~100 km

Dy VI. Slope = m = ________ Dx (x2, y2) = (x1, y1) = ( , ) Steps: 1. Draw a best fit line using a __________ Use two points on the line to calculate m: Steps: 1. Draw a best fit line using a __________ Use two points on the line to calculate m: (x2, y2) = ( , ) ruler 8 32 40 30 m = Dy = Dx = ________ = y2 – y1 x2 – x1 20 32 - 5 8 - 1 10 (x1, y1) = ( , ) 1 5 3.9 2 4 6 8

In PhysRT: