1 / 33

Chapter 2

Chapter 2. Measurements and Calculations. 2.2 Units of Measurement. Nature of Measurement. Measurement - quantitative observation consisting of 2 parts. Part 1 – number Part 2 - scale (unit) Examples: 20 grams 6.63 x 10 -34 Joule*seconds.

dena
Download Presentation

Chapter 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 2 Measurements and Calculations 2.2 Units of Measurement

  2. Nature of Measurement Measurement - quantitative observation consisting of 2 parts • Part 1 – number Part 2 - scale (unit) • Examples: • 20grams • 6.63 x 10-34Joule*seconds

  3. The Fundamental SI Units(le Système International, SI)

  4. Derived Units • Volume: Liter - non SI unit commonly used • 1 liter = 1 cubic decimeter 1 liter = 1000 ml = 1000 cm3 • Density: kg/m3 is inconveniently large commonly used unit is g/cm3 or g/ml 1 g/cm3 = 1 g/ml • gas density is reported in g/liter

  5. Specific Gravity • A comparison between a substance’s density and that of water, at a specified temperature and pressure. • Since density is divided by density, specific gravity is a dimensionless quantity, meaning it has no units. • It is common to use the density of water at 4 °C (39 ° F) as reference - at this point the density of water is at the highest - 1000 kg/m3.

  6. Metric Prefixes

  7. Conversions: Factor-Label Method (Dimensional Analysis) Conversion Factor Number, Desired Unit Starting Number, Unit X Number, Starting Unit

  8. Practice D = 3.65 g/cm3 • What is the density of a sample of ore that has a mass of 74.0 g and occupies 20.3 cm3? • 2) Find the volume of a sample of wood that has a mass of 95.1 g and a density of 0.857 g/cm3. • 3) Express a time period of exactly 1.00 day in terms of seconds. • 4) How many centigrams are there in 6.25 kg? V = 111 cm3 t = 86400 s m = 625000 cg

  9. Chapter 2 Measurements and Calculations 2.3 Using Scientific Measurement

  10. Uncertainty in Measurement • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

  11. Why is there uncertainty? • Measurements are performed with instruments • No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?

  12. Precision and Accuracy • Accuracyrefers to the agreement of a particular value with the truevalue. • Precisionrefers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

  13. Types of Error • Random Error(Indeterminate Error) - measurement has an equal probability of being high or low. • Systematic Error(Determinate Error) - Occurs in the same directioneach time (high or low), often resulting from poor technique or incorrect calibration.

  14. Percent Error • A way to compare the accuracy of an experimental value with an accepted value. • Percent = Value accepted – Value experimental x 100 • Error Value accepted • Ex: The actual density of a certain material is 7.44 g/cm3. A student measures the density of the same material as 7.30 g/cm3. What is the percentage error of the measurement? % Error = 1.9 %

  15. Rules for Counting Significant Figures • Nonzero integersalways count as significant figures. • 3456has • 4sig figs.

  16. Rules for Counting Significant Figures • Zeros • Leading zeros do not count as significant figures. • 0.0486 has • 3 sig figs.

  17. Rules for Counting Significant Figures • Zeros • Captive zeros always count as significant figures. • 16.07 has • 4 sig figs. Also known as the Hugging Rule!

  18. Rules for Counting Significant Figures • Zeros • Trailing zerosare significant only if the number contains a decimal point. • 9.300 has • 4 sig figs.

  19. Rules for Counting Significant Figures • Exact numbershave an infinite number of significant figures. • 1 inch = 2.54cm, exactly

  20. Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 5 sig figs 100,890 L  3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

  21. Rules for Rounding

  22. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# of sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  23. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 0.3588 g/mL 0.359 g/mL 1.030 g ÷ 2.87 mL

  24. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 18.734  18.7 (3 sig figs)

  25. Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

  26. Scientific Notation A method of representing very large or very small numbers • M x 10n • M is a number between 1 and 9 • n is an integer • all digits in M are significant • Reducing to Scientific Notation • Move decimal so that M is between 1 and 9 • Determine n by counting the number of places the decimal point was moved Moved to the left, n is positive Moved to the right, n is negative

  27. Mathematical Operations Using Scientific Notation • Addition and subtraction • Operations can only be performed if the exponent on each number is the same Multiplication • M factors are multiplied • Exponents are added Division • M factors are divided • Exponents are subtracted (numerator - denominator)

  28. Operations with Units • Cancellation occurs with the units in the same way that it occurs with numbers common to both the numerator and denominator • Units are handled algebraically, just like numbers • Analysis of units can be a clue as to whether a problem was set up correctly • Calculations involving units must have the correct units shown throughout the working of the problem and attached to the answer

  29. Direct Proportions • The quotient of two variables is a constant k = y/x • As the value of one variable increases, the other must also increase • As the value of one variable decreases, the other must also decrease • The graph of a direct proportion is a straight line

  30. Inverse Proportions • The product of two variables is a constant k = xy • As the value of one variable increases, the other must decrease • As the value of one variable decreases, the other must increase • The graph of an inverse proportion is a hyperbola

  31. Practice D = 1.41 g/mL • Calculate the density of a liquid given that 41.4 mL of it has a mass of 58.24 g. • 2) How many kilometers are there in 6.2 x 107 cm? • 3) How m\any hours are there in exactly 3 weeks? 6.2 x 102 km 504 hours

More Related