1. Math tools: I.__________________ figures (digits) - tell you how ___________ a measurement is - _________ figures  ________ precise Ex: It is not that useful to say that your height is ______________________ inches because your height _____________ by at least an ____________ during the day. precise more 6 ft, 2 and 7/16 changes 1/8 inch Significant

2. Ex 1: Measure the length of a box: L L = 4.7 cm last digit is _____________ 12 3 4 5 6 = 4.7 ±0.1 cm estimated

3. Ex 2: Use a “better” ruler: L L = 4.67 cm last digit is ______________ 12 3 4 5 6 = 4.67 ± estimated 0.01 cm

4. Ex 3: Measure the length of a different box: L L = 6.49 cm = 6.49 ± 12 4 5 6 7 The precision is worthless because answer is _____________—not close to true or actual value. inaccurate 0.01 cm

5. A. Figures (numbers) are significant if they are: 1. ________________ numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 2. any zeros that are: a/ between any _________________ numbers: 5 0 9; or b/ to the ___________ of a non-zero number AND to the ___________ of the decimal point: 0.0079 0 ; or c/ between a non-zero number and the __________ _________ : 1 0. number # sig. figs. number # sig. fig. 5.36.6070 2029003.00 x 10 8 0.00840 0.6740. 2 4 1 2 5 3 Ex: 2 1 significant right decimal point non-zero

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

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

8. Ex: Convert to standard scientific notation numberscientific notation 43000 0.0290 2012 0.5 80 80. 4.3 x 10 4 2.90 x 10 -2 2.012 x 10 3 5 x 10 -1 8 x 10 1 8.0 x 10 1

9. III. Units: In Regents Physics, we almost always use the _____ (International System) metric system. The ___________________,or most basic, units in this system are: SI quantityunit abbrev- iation lengthmeter currentampere timesecond masskilogram m A s kg The abbreviations spell _______________ (almost) "mAsk" fundamental

11. IV. 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 ____ with prefixwithout 5.3 km 1.7 cm 2.00  s 1.21 GW 8.6 kg A trick b/c kg is already an SI unit __________ for length (meters)

13. IV. 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 symbol SI unit prefix _________ represents ____ 10 -9 with prefixwithout 5.3 km 1.7 cm 2.00  s 1.21 GW 8.6 kg 5.3 x 10 3 m 1.7 x 10 -2 m 2.00 x 10 -6 s 1.21 x 10 9 W 8.6 kg A trick b/c kg is already an SI unit __________ for length (meters)

14. 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 _______. Write: 60 mi x _________ = km 96.54 ~100 km 1.609 km 1 mi 1.609 1.609 km 1 mi 1.609 km 1 mi one actual value

15. VI. Slope = m = ________ yy xx 10 20 40 30 24 68 Steps: 1. Draw a best fit line using a __________ 2.Use two points on the line to calculate m: m =  y =  x = ________ = y 2 – y 1 x 2 – x 1 (x 2, y 2 ) = (, ) (x 1, y 1 ) = (, ) 8 32 1 5 0 0 ruler Steps: 1. Draw a best fit line using a __________ 2.Use two points on the line to calculate m: 32 - 5 8 - 1 3.9

16. In PhysRT: