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Understanding Scientific Notation, Accuracy, and Measurements in Chemistry

This guide explores the application of mathematical concepts in chemistry with a focus on scientific notation, accuracy, precision, significant figures, and unit conversions. Learn how to represent large or small numbers concisely, calculate percent error, and recognize significant digits. It also covers density calculations and temperature conversions from Celsius to Kelvin. Practical examples illustrate multiplication and addition of measurements while emphasizing the importance of significant figures. Finally, the guide includes metric practice problems and tips for effective data graphing.

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Understanding Scientific Notation, Accuracy, and Measurements in Chemistry

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  1. Data Analysis Applying Mathematical Concepts to Chemistry

  2. Scientific Notation • concise format for representing extremely large or small numbers • Requires 2 parts: • Number between 1 and 9.99999999… • Power of ten • Examples: • 6.02 x 1023 = 602,000,000,000,000,000,000,000 • 2.0 x 10 -7 m = 0.0000002 m • Use calculator to solve problems on p. 788-789

  3. Accuracy- closeness of measurements to the target value Error- difference between measured value and accepted value (absolute value) Precision- closeness of measurements to each other Accuracy vs Precision

  4. Percent Error • %error = (accepted-experimental) x 100 accepted • EX: The measured mass is 5.0g. It was predicted that the accepted value should have been 6.0 g. • % error = 6.0g-5.0g x 100 = 16.7% 6.0g

  5. Significant Figures • Measurements are limited in their sensitivity by the instrument used to measure

  6. Estimating Measurements • Read one place past the instrument • 35.0 mL is saying the actual measurement is between 34.9 and 35.1 mL

  7. Why Significant Figures? • Measurements involve rounding • Multiplying/dividing or adding/subtracting measurements can not make them more accurate • Provide a way to tell how sensitive a measurement really is… • 5 ≠ 5.0 ≠ 5.00 ≠ 5.000

  8. Recognizing Significant Digits • 1. Nonzero digits are always significant • 543.21 meters has 5 significant figures • 2. Zeros between nonzeros are significant • 505.05 liters has 5 sig figs • 3. Zeros to the right of a decimal and a nonzero are significant • 3.10 has 3 sig figs

  9. Recognizing Sig Figs • 4. Placeholder zeros are not significant • 0.01g has one sig fig • 1000g has one sig fig • 1000.g has four sig figs • 1000.0g has five sig figs • 5. Counting numbers and constants have infinite significant figures • 5 people has infinite sig figs

  10. Rule for Multiplying/Dividing Sig Figs • Multiply as usual in calculator • Write answer • Round answer to same number of sig figs as the lowest original operator • EX: 1000 x 123.456 = 123456 = 100000 • EX: 1000. x 123.456 = 123456 = 123500

  11. Practice Multiplying/Dividing • 50.20 x 1.500 • 0.412 x 230 • 1.2x108 / 2.4 x 10-7 • 50400 / 61321

  12. Rule for Adding/Subtracting • Round answer to least “precise” original operator. • EX: 1000 + 1.2345 1000

  13. Practice Adding/Subtracting • 100.23 + 56.1 • .000954 + 5.0542 • 1.0 x 103 + 5.02 x 104 • 1.0045 – 0.0250

  14. Units of Measure • SI Units- scientifically accepted units of measure: • Know: • Length • Volume (m3) • Mass • Density (g/mL) • Temperature • Time

  15. The Metric System

  16. Metric Practice • 623.19 hL = __________ L • 1026 mm = ___________cm • 0.025 kg = ___________mg • Online Powers of 10 Demonstration: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

  17. Good Info to Know • Volume- amount of space an object takes up (ex: liters) • V = l x w x h • 1 cm3 = 1 mL by definition

  18. More Good Info to Know • Mass is different from weight • Mass ≠ Weight • Mass= measure of the amount of matter in an object • Weight= force caused by the pull of gravity on an object • ***Mass is constant while weight varies depending on the location of an object***

  19. Temperature Scales

  20. Degrees Celsius to Kelvin Tkelvin=Tcelsius + 273 EX: 25 °C = ? K Tkelvin=25 +273=298K Kelvin to Degrees Celsius Tcelsius=Tkelvin - 273 EX: 210 K = ? °C Tc= 273–210= -63°C Temperature Conversions

  21. Derived Quantities- Density • Density- how much matter is in the volume an object takes up. • Density = mass/volume • D= g/mL

  22. Determining Density • Mass- measure in grams with balance • Volume- • Regular shaped object: measure sides and use volume formula • EX: rectangle  V= l x w x h • Irregular shaped object: water displacement

  23. Density by Water Displacement • Fill graduated cylinder to known initial volume • Add object • Record final volume • Subtract initial volume from final volume • Record volume of object

  24. Graphing Data How Does Volume Impact Temperature? • General Rules • Fit page • Even scale • Best fit/trendline • Informative Title • Labeled Axes

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