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Using and Expressing Measurements

3.1. Using and Expressing Measurements. Using and Expressing Measurements How do measurements relate to science?. 3.1. Using and Expressing Measurements. A measurement is a quantity that has both a number and a unit.

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Using and Expressing Measurements

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  1. 3.1 Using and Expressing Measurements • Using and Expressing Measurements • How do measurements relate to science?

  2. 3.1 Using and Expressing Measurements • A measurement is a quantity that has both a number and a unit. • it is important to be able to make measurements and to decide whether a measurement is correct.

  3. Scientific Notation • http://www.youtube.com/watch?v=H578qUeoBC0 • Scientific Notation Pre-Test

  4. Scientific Notation • 210, 000,000,000,000,000,000,000 • This number is written in decimal notation. When numbers get this large, it is easier to write it in scientific notation • Where is the decimal in this number?

  5. 210, 000,000,000,000,000,000,000. • Decimal needs moved to the left between the 2 and the 1 ( numbers that are between 1-10) • When the original number is more than 1 the exponent will be positive. • 2.1 x 1023 • Exponents show how many places decimal was moved

  6. Express 4.58 x 106 in decimal notation • Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right • 4,580, 000

  7. express the number 0.000000345 in scientific notation. • Decimal moved between first 2 non-zero digits and will be moved 7 times • 3.45 x 10 -7 • The exponent is negative because the original number is a very small number

  8. Express the following in scientific notation or standard notation • 1. 74171.7 2. .07882 • 3. 526 4. .0000573 • 5. 5.8 x 10 -7 6. 5.256 x 106

  9. 3.1 Accuracy, Precision, and Error • Accuracy, Precision, and Error • What is the difference between accuracy and precision?

  10. 3.1 Accuracy, Precision, and Error • Accuracy and Precision • Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. • Precision is a measure of how close a series of measurements are to one another.

  11. 3.1 Accuracy, Precision, and Error • To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. • To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

  12. 3.1 Accuracy, Precision, and Error

  13. 3.1 Accuracy, Precision, and Error • Determining Error • The accepted (Known) value is the correct value based on reliable references. • The experimental value is the value measured in the lab. • The difference between the experimental value and the accepted value is called the error.

  14. 3.1 Accuracy, Precision, and Error • The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%. Experimental – known

  15. 3.1 Accuracy, Precision, and Error • Percent Error • (Error) 3.00-measurement X 100 • 3.00

  16. 3.1 Accuracy, Precision, and Error • Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

  17. REVIEW

  18. REVIEW

  19. % ERROR • The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error? • What is 5.256X10-6 in standard format • What is 118000 in scientific notation

  20. 3.1 Significant Figures in Measurements • All measurement contains some degree of uncertainty. • The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. • Measurements must always be reported to the correct number of significant figures • Using pages 66-72 – fill in your notes regarding the rules of significant figures

  21. Counting Significant Figures Number of Significant Figures • 38.15 cm 4 • 5.6 ft 2 • 65.6 lb ___ • 122.55 m ___ • Complete: All non-zero digits in a measured number are (significant or not significant). Timberlake lecture plus

  22. Leading Zeros Number of Significant Figures • 0.008 mm 1 • 0.0156 oz 3 • 0.0042 lb ____ • 0.000262 mL ____ • Complete: Leading zeros in decimal numbers are (significant or not significant). Timberlake lecture plus

  23. Sandwiched Zeros Number of Significant Figures • 50.8 mm 3 • 2001 min 4 • 0.702 lb ____ • 0.00405 m ____ • Complete: Zeros between nonzero numbers are (significant or not significant). Timberlake lecture plus

  24. Trailing Zeros Number of Significant Figures25,000 in. 2 • 200 yr 1 • 48,600 gal 3 • 25,005,000 g ____ • Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders. Timberlake lecture plus

  25. Learning Check • A. Which answers contain 3 significant figures? • 0.4760 2) 0.00476 3) 4760 • B. All the zeros are significant in • 1) 0.00307 2) 25.300 3) 2.050 x 103 • C. 534,675 rounded to 3 significant figures is • 1) 535 2) 535,000 3) 5.35 x 105 Timberlake lecture plus

  26. Significant Figures in Calculations • A calculated answer cannot be more precise than the measuring tool. • A calculated answer must match the least precise measurement. • Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing Timberlake lecture plus

  27. Adding & Subtracting • The answer has the same number of decimal places as the measurement with the fewest decimal places. • 25.2one decimal place • + 1.34two decimal places • 26.54 • answer 26.5 one decimal place Timberlake lecture plus

  28. Learning Check • In each calculation, round the answer to the correct number of significant figures. • A. 235.05 + 19.6 + 2.1 = • 1) 256.75 2) 256.8 3) 257 • B. 58.925 - 18.2 = • 1) 40.725 2) 40.73 3) 40.7 Timberlake lecture plus

  29. Solution • A. 235.05 + 19.6 + 2.1 = • 2) 256.8 • B. 58.925 - 18.2 = • 3) 40.7 Timberlake lecture plus

  30. Multiplying and Dividing • Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Timberlake lecture plus

  31. Multiplication + Division • Answer should have the same number of significant figures as the measurement with the least. • You may need to round your answer in order to achieve this

  32. Learning Check • A. 2.19 X 4.2 = • 1) 9 2) 9.2 3) 9.198 • B. 4.311 ÷ 0.07 = • 1)61.582) 62 3) 60 • C. 2.54 X 0.0028 = • 0.0105 X 0.060 • 1) 11.3 2) 11 3) 0.041 Timberlake lecture plus

  33. Solution • A. 2.19 X 4.2 = 2) 9.2 • B. 4.311 ÷ 0.07 = 3) 60 • C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060 • Continuous calculator operation = • 2.54 x 0.0028  0.0105  0.060 Timberlake lecture plus

  34. 3.1 Significant Figures in Calculations • Rounding • To round a number, you must first decide how many significant figures your answer should have. • Your answer should be rounded to the number with the least amount of significant figures

  35. QUIZ • How many significant figures are in the number • 603.040 b. 0.0828 c. 690,000 2. Perform the following operations and report to the correct number of sig. figs • 4.15 cm X 1.8 cm • 36.47 + 2.721 + 15.1 • 5.6 x 107 x 3.60 x 10-3

  36. 3.1

  37. 3.1

  38. 3.2

  39. 3.2

  40. 3.3

  41. 3.3

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