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Scientific Measurement

Scientific Measurement. Chapter 3 Sections 1, 3, and 4. Measurements and Their Uncertainty. Measurement  a quantity that has both a number and a unit NO NAKED NUMBERS!! In science we often deal with very large or very small numbers…

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Scientific Measurement

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  1. Scientific Measurement Chapter 3 Sections 1, 3, and 4

  2. Measurements and Their Uncertainty • Measurement  a quantity that has both a number and a unit • NO NAKED NUMBERS!! • In science we often deal with very large or very small numbers… • Scientific notation  an expression of numbers in the form m x 10n where m is equal to or greater than 1 and less than 10, and n is an integer

  3. Measurement • Qualitative vs. Quantitative • Qualitative  descriptive • “My teacher is intelligent” • Quantitative  numeric • “My teacher has an IQ of 185” • Mass vs. weight • Mass  measure of the quantity of matter • Weight  measure of the gravitational pull on matter

  4. Measurement • Density  ratio of mass to volume • Typical units = g/mL • mL = cm3 • Density is dependent of temperature • More dense substances will sink below less dense substances m D = V Density depends on the composition of the sample

  5. Measurement • Practice Problem • You have a metal sample with a density of 2.50 g/cm3. You place the sample on the balance to find that its mass is 624 g. What is the volume of the metal sample? m D = V 624 g V = = 250. cm3 V x D = m 2.50 g/cm3 m V = D

  6. Measurement • Temperature • Fahrenheit (°F) • Boiling point of water = 212°F • Freezing point of water = 32°F • He used the temperature of his wife (96°) to act as the high point on his temperature scale and the temperature of a bath of ice as the zero point • This scale has mostly been replaced by the Celsius scale

  7. Measurement • Temperature • Celsius • Boiling point of water = 100°C • Freezing point of water = 0°C • Kelvin • Boiling point of water = 373.15 K • Freezing point of water = 273.15 K • The Celsius and Kelvin temperature scales are most commonly used, especially in science

  8. Measurement • Conversions between temperature scales • °F = °C x 9/5 + 32 • °C = (°F – 32) x 5/9 • °C = K – 273 • K = °C + 273

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

  10. Accuracy, Precision, and Error • Determining Error Error = experimental value – accepted value • Experimental value  value measured in the lab • Accepted value  correct value based on reliable references • Percent Error = X 100% • Using the absolute value of error means that the percent error will always be a positive value error accepted value

  11. Accuracy, Precision, and Error • Practice Problem • Suppose you use a thermometer to measure the boiling point of pure water at standard pressure. The thermometer reads 99.1°C. You research that the true value of the boiling point of pure water under these conditions is actually 100.0°C. Determine the error and the percent error.

  12. Accuracy, Precision, and Error • Practice Problem Error = experimental value – accepted value Error = 99.1°C – 100.0°C = - 0.9°C Percent Error = X 100% Percent Error = X 100% Percent Error = 0.9% error accepted value 0.9°C 100.0°C

  13. Significant Figures

  14. Significant Figures • All nonzero digits are significant. • Zeros surrounded by nonzero digits are significant. • Leading zeros are insignificant. • Trailing zeros can be either significant or insignificant • Significant if zeros are to the right of a decimal • Significant if zeros are followed by a decimal • Insignificant if zeros are not followed by a decimal • Counted or defined numbers have an unlimited number of significant figures and will not affect the process of rounding an answer

  15. Significant Figures • Practice Problem • Determine the number of significant figures in each of the following values. • 123 m • 9.8000 x 104 m • 0.07080 m • 40,506 mm • 22 meter sticks • 98,000 m • 60.05 3 5 4 5 unlimited 2 4

  16. Rounding Significant Figures • CAUTION!! Calculators rarely use significant figures… • A calculated answer cannot be more precise than the least precise measurements from which it was calculated • You must round your answer to show the correct number of significant figures

  17. Rounding Significant Figures • Rounding Rules… • If the number following the last significant digit is… • Greater than 5: round the last significant figure up • Less than 5: the last significant figure stays the same • Equal to 5 and the last significant figure is not an even number, round up to make it an even number **5 must be the very last number • Equal to 5 followed by any digit rounds up

  18. Rounding Significant Figures • Practice Problem • Round each of the following numbers to 3 significant digits: • 46.17 • 46.11 • 46.15 • 46.45 • 46.451 46.2 46.1 46.2 46.4 46.5

  19. Significant Figures for Mathematical Operations • Addition & Subtraction • Final answer must have the same number of significant figures to the right of the decimal as the number with the fewest digits to the right of the decimal used to calculate the answer 25.1 + 2.621 = 27 + 3.75 + 30.75 = 27.7 1 3 62 0 2 2

  20. Significant Figures for Mathematical Operations • Multiplication & Division • Final answer must have the same number of significant digits as the number with the least significant digits used to calculate the answer 2.0 x 132 = 260 2 3 4 87.65 = 42.3 2.07 3

  21. Scientific Notation • Scientific notation simplifies large and small numbers M x 10n (Where M is between 1 and 10 and n is a whole number) 24000  2.4 x 104 The following few slides should be a review!!

  22. Scientific Notation • As you move the decimal to the right, n decreases 5.2 x 104 52000. x 100  52000 0.0919  0.0919 x 100  9.19 x 10-2

  23. Scientific Notation • As you move the decimal to the left, n increases 5.2 x 10-4 0.00052 x 100  0.00052 3570.  3570. x 100  3.570 x 103

  24. Operations with Scientific Notation • Addition & Subtraction • The value of n must be the same for all numbers 4.5 x 103 + 5.2 x 102 4.5 x 103 + 0.52 x 103 = 5.02 x 103 OR 45 x 102 + 5.2 x 102 = 50.2 x 102

  25. Operations with Scientific Notation • Multiplication • Multiply M values and add n values (5 x 102) x (8 x 103) = 40 x 105 = 4 x 106 5 x 8 = 40 and 2 + 3 = 5 • Division • Divide M values and subtract n values 7.2 x 105 8.0 x 102 7.2 = 0.90 and 5 – 2 = 3 8.0 0.90 x 103 9.0 x 102

  26. Conversion Problems • Conversion factor  a ratio of equivalent measurements • Recall that the number of significant figures in our final answer is NOT dependent on the number of significant figures within a conversion factor • Any equality can become a conversion factor 12 inches 1 foot 12 inches = 1 foot OR 1 foot 12 inches

  27. Conversion Problems • Dimensional Analysis  provides an alternative approach to problem solving • Dimensional analysis uses conversion factors to convert between units • When using conversion factors, set up the ratio so that old units will cancel 125 feet = ? inches 12 inches 125 feet x = 1500 in = 1.50 x 103 in 1 foot

  28. Conversion Problems • Practice Problem • How many miles are in 6.25 km if 1 mile is equivalent to 1.61 km? 1 mile 1.61 km

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