Significant Figures and Scientific Notation

100 mL Graduated Cylinder Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

Significant Figures, Rules for Determining Significant Figures Nonzero digits are always significant. Zeros between nonzero digits are significant. 3. Zeros in front of nonzero digits are not significant. 4. Zeros both at the end of a number and to the right of a decimal point are significant. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant Figures, continued Rules for Determining Significant Figures, continued Zeros both at the end of a number but to the left of a decimal point may not be significant. If a zero has not been measured or estimated, it is not significant. A decimal point placed after zeros indicates that the zeros are significant. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant figures: Rules for zeros Leading zeros are not significant. Leading zero 0.421 – three significant figures Captive zeros are significant. Captive zero 4012 – four significant figures Trailing zeros are significant. Trailing zero 114.20 – five significant figures

Significant Figures Counting Sig Figs Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Counting Sig Fig Examples Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g → 7.9 mL → 354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Scientific Method

Scientific Notation In science, we often work with very large or very small numbers: Ex: Speed of Light = 300,000,000 m/s Avg speed of snail = 0.00086 m/s So we don’t have to be repetitive and write out the zeroes, we use Scientific Notation Express numbers as: 1) A number between 1 and 10 2) Power of 10

Scientific Notation 300,000,000 = 3.0 x 108 0.00086 = 8.6 x 10-4 The power of 8 tells us that the decimal point is actually 8 places to the right 0.00086 = 8.6 x 10-4 The power of NEGATIVE 4 tells us that the decimal place is 4 places to the left Scientific Notation makes very large or very small numbers easier to work with

Calculations using Scientific Notation When multiplying we multiply the actual number and add the exponents (3.0 x 108 m/s) x (5.0 x 102 s) = 15 x 1010 m = ? When dividing we divide the actual numbers and subtract the exponents 1.5 x 1011 m = 1.5 x 1011 – 8s = 0.50 x 103 s = ? 3.0 x 108 m/s 3.0