PREREQUISITES!!! Lecture Homework: Reading - Chapter 2, sections 5-8 Problems from chapter 2, DUE MONDAY #’s 5, 7, 8, 11, 13, 33, 35, 37, 38, 39, 40, 43, 45, 47-52 (all) Lab Homework – Experiment #1 Read intro and lab CAREFULLY PREREQUISITES!!!

Uncertainty All about uncertainty ALL measurements have some uncertainty between 11.5 and 12 cm about 11.83 cm about 11.7 or 11.8 cm

Uncertainty Time’s up!! 5:02 5:01 5:00

Uncertainty All about uncertainty ALL measurements have some uncertainty about 11.8 cm

Uncertainty All about uncertainty ALL measurements have some uncertainty

Uncertainty Exact numbers: Examples: 1 foot = 1 kilometer = 1 mile = 24 hours = Have NO uncertainty because these numbers are DEFINED Will never affect “significant figures”

Uncertainty Counted numbers: Examples Also have no uncertainty I have 11 fingers there are 11 dogs Also have no uncertainty Will never affect “significant figures”

Uncertainty Measured number ALWAYS have some uncertainty to them Examples I live 6 and a half miles away I drink 1.5 liters of water a day This bench is… ALWAYS have some uncertainty to them Will always affect “significant figures”

Uncertainty and Measurements State the digits you can be sure of! Guess the next digit! (and only the next digit) I KNOW it is between 11 cm and 12 cm measurement: 11.8 cm graduations (marks): 1 cm uncertainty: ± 0.1 cm

Uncertainty and Measurements State the digits you can be sure of! Guess the next digit! (and only the next digit) I KNOW it is between 11.8 cm and 11.9 cm measurement: 11.84 cm graduations (marks): 0.1 cm uncertainty: ± 0.01 cm

Uncertainty and Measurements State the digits you can be sure of! Guess the next digit! (and only the next digit) between 500 cm and 600 cm measurement: 520 cm graduations (marks): 100 cm uncertainty: ± 10 cm

Uncertainty and Measurements If your instrument has an uncertainty of ± 0.01 mL, your measurement will end with .00 .01 .02 .03 .04 .05 .06 .07 .08 or .09 If your instrument has an uncertainty of ± 0.2 g, your measurement will end with .0 .2 .4 .6, or .8 If your instrument has an uncertainty of ± 0.005 cm, your measurement will end with .000 or .005

Uncertainty and Measurements Which of the following would be correct if measured on the ruler below? assume ± 0.1 cm uncertainty a) 1.0 cm b) 1.50 cm c) 1.55 cm d) 1.6 cm e) 2.00 cm

Uncertainty and Measurements Which of the following would be correct if measured on the ruler below? (This ruler has an uncertainty of ± 0.05 cm) a) 0.5 cm b) 0.50 cm c) 0.055 cm d) 0.75 cm e) 0.100 cm

11.84 cm Significant Figures 4 significant figures Significant figures tell you about the uncertainty in a measurement. Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit 11.84 cm 4 significant figures

520 cm Significant Figures 2 significant figures Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit 520 cm 2 significant figures

How many Sig. Figs.? Two rules: #1) If there IS a decimal point in the number: Start at right of number and count until the LAST non-zero digit

2 3 . 2 8 1 . 6 8 1 . How many Sig. Figs.? 9 significant figures 2 8 1 9 significant figures . 6 8 4 significant figures 1 . 6 significant figures

How many Sig. Figs.? Two rules: #1) If there IS a decimal point in the number: Start at right of number and count until the LAST non-zero digit #2) If there is NOT a decimal point in the number Start at left of number and count until the LAST non-zero digit

7 4 2 9 3 2 3 8 1 How many Sig. Figs.? 5 significant figures 8 4 significant figures 1 1 significant figure

Significant Practice 60020300 12.00500 0.0005 0.10046 320000 8900. 0.0061000 0.1528 6 s.f. 7 s.f. 1 s.f. 5 s.f. 2 s.f. 4 s.f.

Rounding Numbers Find the last significant digit. If the next digit to the right is 4 or less, leave the last significant digit alone. If the next digit to the right is 5 or more, round the last significant digit up. Put large numbers into scientific notation BEFORE rounding

0.00259428 (3 s.f.) 0.00259428 (3 s.f.) = 0.00259 54.3675701 (5 s.f.) 54.3675701 (5 s.f.) = 54.368 8265391000 (2 s.f.) 8265391000 (2 s.f.) = 8300000000 0.659822 (3 s.f.) 0.659822 (3 s.f.) = 0.66 = 0.660 0.0005473300 (5 s.f.) 0.0005473300 (5 s.f.) = 0.00054733 617890100 (5 s.f.) 617890100 (5 s.f.) = 617890000

Sig. Figs. in Calculations Two rules: #1) Multiplication and Division The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.

Calculations with Sig. Figs. Multiplication and division The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. 1.5 x 7.3254 = 1 .9881 = 11 2 s.f. 5 s.f. 6.127 x 0.0000267030 = 0.000163 6 09 = 0.0001636 4 s.f. 6 s.f.

Calculations with Sig. Figs. 927.381 / 456.0 = 2.03 3 730263 = 2.034 6 s.f. 4 s.f. 0.00159 / 2 = 0.000 7 95 = 0.0008 3 s.f. 1 s.f. 6 s.f. 3 s.f. = 18 8 99522.37 = 18900000 4 s.f.

Some Practice 890.00 x 112.3 78132/2.50 0.0120 x 48.15 x 0.0087 500 x 0.000230012 99950 31300 0.0050 0.000000025 1900000 0.1

Sig. Figs. in Calculations Two rules: #1) Multiplication and Division: The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. #2) Addition and Subtraction: The value in the calculation that has the FEWEST decimal spots determines the number of decimal spots in your answer.

Adding and subtracting with sig. figs. 0.0025647 + 0.000321 7 decimal places 6 decimal places 0.0025647 0.0025647 +0.000321_ +0.000321_ 0.0028857 0.0028857 = 0.002886 answer can only be precise to the 6th decimal place

Adding and subtracting with sig. figs. 394.0150 + 0.0074121 4 decimal places 7 decimal places 394.0150 394.0150 + 0.0074121 + 0.0074121 394.0224121 394.0224121 = 394.0224 answer can only have 4 decimal places

Some More Practice 23.67 – 75 5502.8 + 24 + 0.01 0.109 + 0.09 – 0.955 20.4 + 1.322 + 78 -51 5527 -0.76 100.

Sig. Figs. in Calculations Two rules: #1) Multiplication and Division: The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. #2) Addition and Subtraction: The value in the calculation that has the FEWEST decimal spots determines the number of decimal spots in your answer.

Mixed Operations with sig. figs. 1) Do inside parenthesis first 2) Mark the last significant digit you are going to keep in that step 3) Finish calculations 4) Report answer to correct number of sig. figs. 4 sig. figs.   5 sig. figs.