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Understanding Scientific Measurements and Notation

Explore the importance of measurements in science, focusing on accuracy, precision, and significant figures. Learn how to express quantities using scientific notation and practice calculations.

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Understanding Scientific Measurements and Notation

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  1. Scientific Measurement Chapter 3

  2. Introduction • Measurements are key to any scientific endeavor, including chemistry. • All measurements have a numerical component and a unit component. • The numerical component of a measurement must report the precision of the instrument. • The SI system of unit is used in the sciences. • Conversion factors, like density, allows us to convert from one unit to another.

  3. Measurements and Their Uncertainty(Section 3.1) • Using and Expressing Measurements • Accuracy, Precision, and Error • Significant Figures in Measurements • Significant Figures in Calculations

  4. I.) Using and Expressing Measurements • Measurements are used to determine the magnitude of some quantity, like mass or volume. • Measurements are a central part of all the sciences. • Therefore, an important characteristic of a measurement is that it must be understood by anyone who looks at it.

  5. What is a Measurement? A quantity that has both a number and a unit. • Examples: • 5.54 mL • 3.00 x 108 m/s (speed of light in a vacuum) • 9.3 x 106 miles (distance to the sun) • 6.02 x 1023 mol-1 (Avogadro’s Number)

  6. What are the parts of a measurement? A quantitative description has both a number and a unit. We know what numbers are and how to represent them, but what about units?

  7. Scientific Notation A number written as the product of two numbers: a coefficient and a 10 raised to a power. • This method of writing numbers is often used to • express very large or very small values. • Examples: • 5.98 x 10 24 kg (mass of the Earth) • 9.11 x 10-28 g (mass of an electron)

  8. Coefficient: This number is always greater than or equal to 1 and less than 10. • Exponent: This value tells you how many times the coefficient must be multiplied or divided by 10 to equal the magnitude of the original number.

  9. How to Write in Scientific Notation • For large numbers: - start counting at the decimal point - move towards the left - stop right before the last digit - the number of “spaces” moved is the exponent (expressed as a positive number)

  10. For small numbers: - Start counting at the decimal point - Move towards the right. - Stop when you pass the first non-zero digit. - the number of “spaces” moved is the exponent (expressed as a negative number)

  11. Let’s practice this. Write the following numbers in scientific notation: 1.) 6,300,000 2.) 0.0000008 3.) 0.0000736

  12. Now let’s write the standard form for each of the following number in scientific notation. • 4 x 10-3 • 5.4 x 106 • 2.7 x 10-7 • 8.9 x 103

  13. Adding and Subtracting Numbers in Scientific Notation • Easiest way is to enter the numbers into you calculator. You must know how to use scientific notation on your calculator. • If you don’t have a calculator: • Make sure the exponents are the same. • Add/subtract the coefficients. • Keep the exponent the same.

  14. Multiplying and Dividing Numbers in Scientific Notation • Easiest way is to enter the numbers into you calculator. You must know how to use scientific notation on your calculator. • If you don’t have a calculator: • For multiplying • Multiply coefficients • Add exponents • For dividing • Divide the coefficients • Subtract the exponents

  15. Let’s practice. Add, Subtract, Multiply, or Divide. • (3 x 104) x (2 x 102) = • (3.0 x 105) ÷ (6.0 x 102) = • (8.0 x 102) + (5.4 x 103) = • (3.42 x 10-5) – (2.5 x 10-6) =

  16. Incredulous Unwilling to admit or accept what is offered as true. 1 Thessalonians 5:21 Test everything. Hold on to the good

  17. II.) Accuracy, Precision, and Error Error is introduced in how we carry out our experiment and how we choose to measure what we observe. Therefore, there is always error in experimentation.

  18. Accuracy and Precision ARE NOT Synonymous in Science AccuracyA measure of how close a measurement comes to the actual value of whatever is measured (i.e. correctness) PrecisionA measure of how close a series of measurements are to one Another (i.e. reproducibility).

  19. What do we strive for in science?

  20. We must express the level of precision our measurements have and always indicate the error inherent in all measurements.

  21. Reporting Error • Error is inherent in all measurements. • Accurate values are difficult to attain and require multiple measurements. • Accepted Value: The “correct” value based on reliable references. • Experimental Value: The value measured in the lab

  22. Error and Percent Error • Error Error = experimental value – accepted value • Percent error Percent error = error /accepted value x 100

  23. Determining Precision • Precision is determined by the instruments used to make a measurement. • Significant figures are used to report precision in a measurement.

  24. III.) Significant Figures in Measurements • The significant figures in a measurement include all of the digits that are known and a last digit that is estimated. • Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

  25. Significant Figures Rule #1 Every nonzero digit in a reported measurement is assumed to be significant. Examples: 1.) 24.7 meters 2.) 0.743 meter 3.) 714 meters 3 significant figures

  26. Significant Figures Rule #2 Zeros appearing between nonzero digits are significant. Examples: 1.) 7003 meters 2.) 40.79 meters 3.) 1.503 meters 4 significant figures

  27. Significant Figures Rule #3 Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. Examples: 1.) 0.0071 meter 2.) 0.42 meter 3.) 0.000000099 meter 2 significant figures

  28. Significant Figures Rule #4 Zeros at the end of a number and to the right of a decimal point are always significant. Examples: 1.) 43.00 meters 2.) 1.010 meters 3.) 9.000 meters 4 significant figures

  29. Significant Figures Rule #5 Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as a placeholder. Examples: 1.) 300 meters 2.) 7000 meters 1 significant figure

  30. Significant Figures Rule #6 There are two situations in which numbers have an unlimited number of significant figures: 1.) Counted quantities 2.) Defined quantities

  31. Let’s practice. Indicate the number of significant figures in each of the following measurements. • 456 mL. • 70.4 m. • 444,000 g. • 0.00406 mg. • 0.90 L. • 56 eggs in a basket • 12 eggs in 1 dozen

  32. IV.) Significant Figures in Calculations A calculated answer cannot be more precise than the least precise measurement from which it was calculated. What does this mean?

  33. Find the measurement with the least number of significant figures and this will tell you how many significant figures you can have in your answer. You will be required to round.

  34. Rounding Rules • Decide how many significant figures the answer should have. • Round to that many digits counting from the left. • If the digit immediately to the right of the last significant digit is less than 5, the value of the last significant figure stays the same. • If the digit immediately to the right of the last significant digit is 5 or greater, the value of the last significant figure is increased by one. • Drop all other digits.

  35. Let’s practice. Round each of measurement to three significant figures. Write your answers in scientific notation. • 87.073 meters • 4.3621 x 108 meters • 0.01552 meter • 9009 meter • 1.7777 x 10-3 meter • 629.55 meters

  36. Significant Figures in Addition and Subtraction Problems The answer to an addition or a subtraction problem should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

  37. Sample Problem Calculate the sum of the three measurements. Give the answer to the correct number of significant figures. 12.52 meters + 349.0 meters + 8.24 meters

  38. Let’s practice. Find the total mass of three diamonds that have masses of 14.2 g., 8.73 g., and 0.912 g.

  39. Significant Figures in Multiplication and Division Problems The product or quotient must have the same number of significant figures as the measurement with the least number of significant figures. Note: In these problems the place of the decimal point has nothing to do with the rounding process

  40. Sample Problem Calculate the product or quotient of the three measurements. Give the answer to the correct number of significant figures. • 7.55 meters x 0.34 meter = • 2.4526 meter ÷ 8.4 =

  41. Let’s practice. Calculate the volume of a warehouse that has inside dimensions of 22.4 meters by 11.3 meters by 5.2 meters (Volume = length x height x width).

  42. The International System of Units(Section 3.2) • Measuring with SI Units • Units and Quantities

  43. I.) Measuring with SI Units What is SI? • It is “Le Systeme International d’Unites” (or The International System of Units) • It is a modified version of the metric system. • Adopted internationally in 1960

  44. Why SI? • It is simple and is widely used in the sciences. • All metric units are based on multiples of 10. • Conversions between units are quite easy. • There are 7 base SI units, 5 of which are commonly used in chemistry.

  45. The 7 Base SI Units

  46. Commonly Used Prefixes

  47. II.) Units and Quantities • Different quantities require different units of measurements. • Length = meter (m) • Volume = liter (L) • Mass = kilogram (kg) • Temperature = Celsius (C) or Kelvin (K) • Energy = joule (J)

  48. Length (cm, m, km) The SI basic unit of length is the meter (m). A meter is about the height of the doorknob to the floor. (Adding the prefixes to the basic unit of length allows us to add scale to it.)

  49. decimeter ~ diameter of an orange kilometer ~ 5 city blocks millimeter ~ thickness of a dime micrometer ~ diameter of bacterial cell

  50. Volume (L, mL, cm3, µL) The SI unit for volume is the cubic meter (m3). A cubic meter (m3) is about the volume of an automatic dishwasher. More often the non-SI unit of liter (L) is used for volume.

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